{"messages": [{"content": "Let t(w) be the second derivative of 847*w**5/20 - 275*w**4/4 + 87*w**3/2 - 27*w**2/2 - w. Let t(y) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let w(m) be the third derivative of -91*m**6/4 + 817*m**5/20 + 627*m**4/8 + 45*m**3 + 11*m**2 - 6. Suppose w(o) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let p(c) = c**3 + 2. Let x(k) = -1435*k**3 - 2348*k**2 - 1194*k - 190. Let j(a) = -5*p(a) - x(a). For the polynomial j(f), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 1755/8*n + 405/8 - 585/8*n**2 - 5775/8*n**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let b(t) = -351*t**3 + 654*t**2 - 103*t - 97. Let d(a) = a**3 + a**2 + a - 2. Let o(f) = 5*b(f) + 5*d(f). Let o(n) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let n(z) be the first derivative of -440*z**4/13 - 196*z**3/3 - 42*z**2 - 144*z/13 + 70. If n(w) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let g(l) = -1200*l**3 + 74*l**2 + 351*l - 81. Let j(k) = 800*k**3 - 50*k**2 - 234*k + 54. Let w(c) = -5*g(c) - 8*j(c). Suppose w(y) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let s(o) be the third derivative of o**6/120 - o**4/24 + 13*o**2. Let t(v) = 2250*v**3 + 1128*v**2 - 190*v - 108. Let b(f) = 10*s(f) - t(f). If b(r) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let d(l) = -2083*l**3 + 1527*l**2 + 352*l - 195. Let x(m) = 6063*m**3 + 844 - 3721*m**3 + 3906*m**3 - 4580*m**2 - 1056*m - 260. Let r(w) = 8*d(w) + 3*x(w). If r(f) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of -891/17*o + 6090/17*o**3 + 108/17 - 57/17*o**2 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of -108/7*t + 1650/7*t**3 - 1035/7*t**2 + 81/7 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -2800/13*p**3 + 266256/13 + 5680*p**2 - 507228/13*p, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let p be (154 - 2/1) + -2. Suppose -585*u - 1135*u**3 + p*u**2 + 3135*u**3 - 128 - 7 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Suppose -2535*q**3 + 195*q**3 + 2868*q + 382*q**2 - 2452*q - 96 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let 116/3*c**2 + 140/3*c**3 - 184/5*c - 96/5 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let m(b) be the second derivative of 90*b**2 - 495/2*b**5 + 285/2*b**3 - 5*b + 0 - 635/12*b**4. Suppose m(c) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let w(u) = -8580*u**3 + 5724*u**2 - 1197*u + 81. Let r(t) = -t. Let q(z) = -18*r(z) - w(z). If q(m) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let c(b) = 2110*b**3 - 960*b**2 - 655*b + 268. Let a(t) = t**3 - t + 1. Let n(z) = 2*a(z) + c(z). Let n(q) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let b(w) = w**3 + w**2 + w + 1. Let i(x) = -1902*x**3 + 1611*x**2 + 45*x - 192. Let a(l) = -12*b(l) - i(l). For a(h) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For -1370*h - 1800/7 - 990*h**3 - 15280/7*h**2 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let u(t) be the third derivative of 77*t**6/5 - 663*t**5/20 + 117*t**4/4 - 27*t**3/2 + 213*t**2. For u(r) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -18207/10*f**2 + 567/10 - 4389*f**3 + 189/5*f = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let k = 1233 + -1230. Suppose 135/7*o + 1115/7*o**2 - 200*o**k - 180/7 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "If -147 - 8638/9*g**2 - 3920/9*g**3 - 2023/3*g = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Let f(c) be the third derivative of -169*c**6/56 + 741*c**5/70 - 765*c**4/56 + 54*c**3/7 + 21*c**2 + 1. For f(a) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let q(u) be the first derivative of 330*u**4 - 229*u**3 - 144*u**2 + 135*u + 115. For the polynomial q(p), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let o(a) = -56*a**5 - 44*a**4 + 18*a**3 + 30*a**2 - 5*a. Let h(p) = 168*p**5 + 133*p**4 - 53*p**3 - 89*p**2 + 16*p. Let z(f) = 3*h(f) + 8*o(f). Let j(y) be the second derivative of z(y). Suppose j(x) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let i(o) = 302*o**2 - o + 2. Let n be i(1). Suppose 48 - 660*l**2 + 60 - 15*l - 1400*l**3 + n*l = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let k(t) = t**3 + 7*t**2 - 2*t - 11. Let y be k(-7). If -9*n + 632*n**3 - 141*n**y + 1407*n**2 - 135 + 1126*n**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let i(n) = -621*n**3 - 469*n**2 + 156*n + 93. Let m(a) = 1243*a**3 + 937*a**2 - 311*a - 185. Let p(l) = -10*i(l) - 6*m(l). Suppose p(j) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let p(c) be the third derivative of 27/5*c**3 - 9/20*c**4 + 0*c + 77/20*c**6 - 8*c**2 - 291/50*c**5 + 0. Suppose p(f) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let g(b) be the second derivative of 3267*b**5/25 + 1793*b**4/5 + 1806*b**3/5 + 162*b**2 - 39*b. Find the value of n + m, where n/m is the second largest root of g(x) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 36*b - 203*b + 287*b - 176*b**3 + 72 + 590*b**2 + 318*b = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let n(m) = -9*m - 150. Let t be n(-17). Find the value of n + m, where n/m is the second largest root of -81/10 - 297/10*u + 207/5*u**2 + 168*u**t = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let t(o) be the first derivative of 462*o**4 + 2417*o**3 - 2889*o**2 + 999*o + 81. Let t(q) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let x(n) be the first derivative of -539*n**4/4 + 301*n**3/3 + 123*n**2/2 - 45*n + 95. If x(y) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let k(a) be the third derivative of 0 + 19*a**2 - 7007/1080*a**6 + 4277/270*a**5 + 26/3*a**3 - 1157/72*a**4 + 0*a. For the polynomial k(t), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let o(w) be the third derivative of 1547*w**6/30 + 2152*w**5/15 - 1255*w**4/6 + 104*w**3 - 32*w**2 - 4. Suppose o(i) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let l(h) be the third derivative of -65*h**6/24 - 7*h**5/3 + 47*h**4/8 + 6*h**3 - 3*h**2 + 6. Suppose l(y) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let m(r) be the third derivative of -r**9/630 - 3*r**8/616 - 81*r**7/12320 - 9*r**6/1760 + 17*r**5/60 - 8*r**2. Let g(a) be the third derivative of m(a). Suppose g(d) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let j(p) = -625*p**3 - 1750*p**2 - 371*p + 990. Let r(c) = -1250*c**3 - 3500*c**2 - 741*c + 1980. Let y(m) = 9*j(m) - 4*r(m). Express the second largest root of y(k) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Let n(y) be the third derivative of 0*y - 1936/105*y**6 + 99/7*y**3 - 352/35*y**5 + 0 + y**2 + 363/28*y**4. If n(p) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let d(z) = 9827*z**3 - 4340*z**2 - 14449*z - 4620. Let p(j) = 2456*j**3 - 1085*j**2 - 3612*j - 1155. Let n(c) = -2*d(c) + 9*p(c). Let n(q) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let c(m) be the first derivative of -1155*m**4/8 + 791*m**3/18 + 1841*m**2/6 + 196*m + 225. For the polynomial c(t), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let i be 658/(-423) + 82/18 + 192/11. Suppose 1575/11*w**3 + i - 555/11*w - 55*w**2 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let j(x) = -9118*x**3 + 12729*x**2 + 14851*x + 2631. Let z(h) = 2279*h**3 - 3182*h**2 - 3713*h - 658. Let u(g) = 2*j(g) + 9*z(g). Express the second largest root of u(a) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let c(s) be the third derivative of -77*s**6/3 + s**5/15 + 103*s**4/2 - 48*s**3 - 10*s**2 + 3*s. For c(h) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let s(c) = -1250*c**3 + 755*c**2 + 455*c - 275. Let r(w) = -w - 15. Let b be r(-12). Let j(t) = -625*t**3 + 378*t**2 + 228*t - 138. Let h(y) = b*s(y) + 5*j(y). Let h(u) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let a = -3315 + 3317. If -411/7*w**a - 1320/7*w**3 + 351/14*w + 54/7 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let u(z) be the second derivative of 143*z**5/2 + 1423*z**4/4 + 327*z**3 + 243*z**2/2 - 2*z - 20. Suppose u(c) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let j be (836/228)/((-1)/(-75)). Suppose 45/4*p + 135/8 - j*p**3 - 1545/8*p**2 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let j(w) be the first derivative of -3135*w**4/4 + 221*w**3 + 603*w**2 + 216*w + 187. If j(n) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let f(l) be the first derivative of 78*l**4 + 687*l**3/14 - 27*l**2/7 - 81*l/14 + 49. Express the second largest root of f(c) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let o(d) be the first derivative of -3185*d**4/32 - 2933*d**3/24 + 7*d**2 + 42*d - 27. For the polynomial o(f), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let v be (-3)/(-4)*4*5/(-30)*-4. For the polynomial 81/23 - 540/23*u**v - 2400/23*u**3 + 324/23*u, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let y be ((-30)/(-40))/(1/284). Let -43*o**2 + 832*o**3 - 13 - 117*o + 49 - y*o**2 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let f(l) be the third derivative of 11*l**8/120 - 257*l**7/2520 - 29*l**6/240 + 3*l**5/10 + 5*l**4/24 - 10*l**2. Let o(v) be the second derivative of f(v). For the polynomial o(u), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of -288 - 874*r**2 + 197*r + 1802*r**2 + 1679*r**2 + 2541*r**3 - 41*r = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Let u(o) be the first derivative of -o**4/4 - o**3/3 - o + 2. Let a(f) = -242*f**3 + 136*f**2 + 93*f - 42. Let h(c) = -2*a(c) - 6*u(c). If h(m) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "If 97*t - 210*t**3 - 331*t + 297*t**2 - 36 - 688*t**2 - 9 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let v(m) be the first derivative of -1925*m**4/17 + 6230*m**3/17 + 63*m**2/17 - 1512*m/17 + 69. Let v(h) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let l(m) be the third derivative of -5*m**8/192 + 97*m**7/1848 + m**6/176 - 9*m**5/88 + 3*m**4/8 - 10*m**2. Let n(s) be the second derivative of l(s). For the polynomial n(d), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let m(x) be the second derivative of -35*x**5/4 + 305*x**4/32 + 15*x**3/4 - 135*x**2/16 - 14*x. For the polynomial m(q), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let z(p) be the second derivative of 13*p**8/48 - 383*p**7/1260 - 29*p**6/120 + 3*p**5/5 + 4*p**4/3 + 12*p. Let h(o) be the third derivative of z(o). If h(x) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let c(u) be the first derivative of -546*u**4 - 312*u**3 + 2457*u**2/16 + 1053*u/8 + 58. Let c(i) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let i(z) = -1313*z**3 - 3160*z**2 - 2113*z - 420. Let m(x) = x**3 - x**2 + 2*x. Let a(u) = i(u) - 7*m(u). Let a(h) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "For -201*k - 132*k**2 - 334*k + 76*k + 3264*k**3 + 0*k - 444*k**2 + 81 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Let w(a) be the second derivative of -663/10*a**3 + 459/10*a**2 + 119*a**5 + 0 - 8*a - 34*a**4. For w(r) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let j(p) be the first derivative of -399*p**4/2 + 507*p**3/4 + 189*p**2/16 - 81*p/4 + 16. If j(t) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Let m(p) be the first derivative of -13*p**7/88 + 76*p**6/165 - 261*p**5/440 + 9*p**4/22 + p**3 - 23. Let l(f) be the third derivative of m(f). Let l(g) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let r(s) be the first derivative of 110*s**4 + 73*s**3 - 36*s**2 - 27*s + 112. Let r(k) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 1841*v**3 + 3536*v**3 - 1496*v + 171*v**3 + 480 - 2900*v**2 + 3441*v**3 - 1905*v**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let n(u) be the second derivative of -1089*u**5/190 + 847*u**4/76 + 27*u**3/19 - 189*u**2/38 + 5*u - 7. Express the second largest root of n(d) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let a(h) be the third derivative of -91*h**6/30 + 599*h**5/135 + 79*h**4/27 - 80*h**3/9 + 93*h**2 - h. For a(p) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let 1617*i**2 + 101*i - 298*i - 16*i - 216 - 165*i + 2904*i**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let w be (-3412)/(-28) + -5 - 1 - 1. For the polynomial 360/7*p + w*p**2 - 352*p**3 - 108/7, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let b(g) be the third derivative of -9*g**6/5 - 83*g**5/44 + 11*g**4/4 + 60*g**3/11 - 174*g**2 + 2*g. For the polynomial b(w), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let x(h) be the second derivative of 35*h**5/2 + 155*h**4/4 + 33*h**3 + 27*h**2/2 + 5*h - 2. If x(r) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Suppose 4*c - 32 = -4*c. Let 11*b**2 + 140 - 3388*b**3 + 464*b + c + 77*b**2 + 340*b = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let r(j) be the third derivative of -5*j**7/182 + 7*j**6/78 + 111*j**5/520 + 9*j**4/52 - j**3 + 14*j**2. Let y(g) be the first derivative of r(g). Let y(l) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let r(f) be the third derivative of -9*f**7/98 - 191*f**6/1680 + 15*f**5/112 + 9*f**4/28 + f**3 + 9*f**2. Let h(x) be the first derivative of r(x). For h(t) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Suppose 7*f - 4*f = 63. If -81 + 165*l**2 + f*l + 195*l + 60*l**2 - 600*l**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -759*g**3 - 3357/10*g**2 - 27/5*g + 81/10, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let v(b) = b**3 - 12*b**2 - 10*b - 5. Let x be v(14). Suppose -135 - 3000*f**2 + 578*f**3 - 1125*f - x*f**3 - 2831*f**3 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let k(s) = -s**3 + s**2 - s + 1. Let f(x) = 314*x**3 + 2055*x**2 + 1114*x**3 + 56 + 520*x - 475*x**2. Let z(g) = 2*f(g) - 4*k(g). Let z(l) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let x(g) be the second derivative of 3146*g**5/35 - 440*g**4/7 - 3904*g**3/21 - 768*g**2/7 + 355*g. Suppose x(r) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Suppose 1320/7*v**2 + 1287/7*v - 297/7 - 1100*v**3 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let f = -11886 - -11888. Express the second largest root of 81/13 + 960/13*g**3 - 576/13*g**f - 135/13*g = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Suppose -216/11 + 312/11*k**2 + 280*k**3 - 936/11*k = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let t(l) be the first derivative of -325*l**4/2 + 580*l**3/3 + 3*l**2 - 72*l - 64. If t(o) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let u(f) be the third derivative of 112*f**6/51 - 1262*f**5/255 + 2*f**4 + 60*f**3/17 + 41*f**2 - 3. For the polynomial u(l), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let i(a) be the third derivative of -91*a**6/25 - 417*a**5/100 + 9*a**4/20 + 27*a**3/10 + 392*a**2. For the polynomial i(r), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let j be (368/20)/((-2)/(-3)). Express the second largest root of -j*v - 230*v**3 - 299*v**2 + 207/5 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 1456*x**3 - 26*x + 1002*x**2 - 27 + 46*x + 79*x = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let u(p) = 1 - 2*p. Let j(r) = 1183*r**3 - 1599*r**2 - 226*r + 126. Let l(m) = -j(m) + 6*u(m). Let l(c) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let u(j) be the second derivative of -8*j**7/5 + 6*j**6/5 + 81*j**5/40 - 27*j**4/8 - 19*j**3/6 - 8*j. Let y(x) be the second derivative of u(x). Find the value of n + m, where n/m is the second largest root of y(w) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let k(i) = -252*i**3 + 77*i**2 + 92*i - 25. Let u(s) = 1009*s**3 - 309*s**2 - 369*s + 99. Let v(r) = -9*k(r) - 2*u(r). Suppose v(b) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let r(a) be the first derivative of 275*a**4/4 - 275*a**3/7 - 99*a**2/2 + 297*a/7 + 7. Express the second largest root of r(o) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 486/11 - 513/11*j - 3195/11*j**2 - 150*j**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "If -35*c + 27 - 160*c**2 - 20*c + 968*c**3 - 5*c**2 - 71*c = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let c(a) = -6165*a**3 + 2570*a**2 + 875*a - 355. Let w(u) = 3080*u**3 - 1283*u**2 - 439*u + 180. Let k(q) = 6159*q**3 - 2565*q**2 - 879*q + 361. Let b(m) = 2*k(m) - 5*w(m). Let g(j) = 5*b(j) - 2*c(j). For the polynomial g(f), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let d be (9/(-21))/((-80)/30184). Express the second largest root of -d*t**3 - 441/10*t**2 + 81/10 + 297/10*t = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Suppose 351*k**2 + 26*k - 27 - 770*k**3 - 6*k + 34*k = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose 0 = -991*p + 1001*p - 360. Express the second largest root of -p*m - 1280/21*m**3 - 576/7*m**2 - 36/7 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let t be (60/(-51))/(40/(-1440)). If -2240/17*k**3 + 456/17*k**2 - 216/17 + t*k = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let c be (2/(-40))/((-9)/(-54)) - (-180780)/2600. Let -108/13 - 2400/13*k**2 - c*k - 2000/13*k**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let 27/2 + 3705/4*j**3 - 1113/8*j**2 - 693/8*j = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Let w(k) be the second derivative of 3549*k**5/50 - 3809*k**4/20 + 1533*k**3/10 - 54*k**2 + k + 36. Express the second largest root of w(s) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let n(g) be the third derivative of -143*g**6/50 - 411*g**5/200 + 171*g**4/80 + 27*g**3/10 + 71*g**2. Find the value of n + m, where n/m is the second largest root of n(w) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let u(c) be the third derivative of 77*c**6/92 - 289*c**5/115 + 261*c**4/92 - 36*c**3/23 + 50*c**2. Suppose u(x) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let k(a) = -1138*a**3 - 383*a**2 + 111*a + 36. Let d(m) be the first derivative of -1137*m**4/4 - 382*m**3/3 + 111*m**2/2 + 36*m - 8. Let c(y) = -6*d(y) + 7*k(y). If c(f) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let -27/5*d - 3393/5*d**2 + 162/5 - 5712/5*d**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let m(a) be the third derivative of 385*a**6/51 + 659*a**5/51 - 945*a**4/34 + 300*a**3/17 - 37*a**2. Let m(q) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let h(l) be the second derivative of -54*l**5/5 - 251*l**4/28 + 69*l**3/14 + 54*l**2/7 + 64*l. Express the second largest root of h(p) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let v(o) be the third derivative of -11/16*o**6 - 9/80*o**4 + 0*o - 27/20*o**3 - 6*o**2 + 51/40*o**5 + 0. For the polynomial v(p), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let o(w) = -548*w**3 + 347*w**2 + 36*w - 29. Let z(c) = 2739*c**3 - 1736*c**2 - 180*c + 146. Let s(f) = 22*o(f) + 4*z(f). Let s(m) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose 5*j = 27 - 2. Let c(x) = -3850*x**3 - 1495*x**2 + 1530*x + 450. Let z(l) = 1925*l**3 + 748*l**2 - 765*l - 225. Let u(p) = j*z(p) + 3*c(p). Find the value of n + m, where n/m is the second largest root of u(a) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let c(d) = -821*d**3 - 686*d**2 + 67*d + 108. Let k = 12 - 9. Let x(b) = -822*b**3 - 687*b**2 + 66*b + 108. Let j(o) = k*c(o) - 4*x(o). For the polynomial j(s), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let y(s) be the first derivative of -55*s**6/3 - 23*s**5 + 6*s**4 + 18*s**3 + 6*s**2 - 7. Let v(r) be the second derivative of y(r). Let v(h) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let k(r) be the first derivative of 75*r**5/26 + 75*r**4/52 - 45*r**3/13 - 81*r**2/26 - 4*r + 3. Let b(p) be the first derivative of k(p). If b(d) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of -176*n**3 - 1122/5 + 6699/5*n**2 - 4697/5*n = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let w(r) be the first derivative of -275*r**4/4 + 25*r**3 + 99*r**2/2 - 27*r - 1. If w(n) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let f(n) be the first derivative of 16*n**6 + 472*n**5/15 - 5*n**4/12 - 28*n**3 - 11*n**2/2 + 31. Let d(t) be the second derivative of f(t). For the polynomial d(g), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let h(k) be the second derivative of 726*k**5/35 + 1023*k**4/28 + 639*k**3/28 + 81*k**2/14 + 5*k + 3. Let h(l) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let g(m) be the third derivative of -49*m**6/12 - 7*m**5/60 + 8*m**4 + 15*m**3/2 + 186*m**2. For g(x) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let u(k) = 18*k + 393. Let n be u(-16). Suppose 81/10 + 279/2*a**2 + 297/5*a + n*a**3 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -1539/17*a - 135/17 - 5205/17*a**2 - 273*a**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let i be 138/(-60) + (1 - -1) + 20670/150. Express the second largest root of -22*x**2 - 3245/6*x + 990*x**3 + i = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose -252/5*k**2 - 96*k**3 + 1674/25*k - 324/25 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose -15143 = -63*i + 4702. For i*x**3 - 81/2*x**2 + 243/10 - 486/5*x = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let c(w) be the third derivative of 11*w**9/10080 - 223*w**8/33600 - w**7/2800 + 3*w**6/200 + w**5/15 + 9*w**2. Let l(a) be the third derivative of c(a). Find the value of n + m, where n/m is the second largest root of l(x) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let g(h) be the first derivative of 105*h**4/2 - 57*h**3 - 183*h**2/5 + 63*h + 125. If g(t) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "If 10241/5*k**3 + 6293/5*k**2 - 126*k - 504/5 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For -1500/17*a**3 - 13689/17 - 15795/17*a + 10800/17*a**2 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let p(o) be the third derivative of 352*o**7/1365 - 32*o**6/195 - 33*o**5/130 + 9*o**4/26 + o**3/2 - 12*o**2. Let y(i) be the first derivative of p(i). For the polynomial y(c), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let s = -6 + 15. For the polynomial -1911*m**3 - 50 + 351*m - 12 + s - 55 + 588*m**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let y(t) be the third derivative of 24/5*t**4 + 206/25*t**5 + 25*t**2 - 36/5*t**3 + 0*t - 154/15*t**6 + 0. Suppose y(l) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let t(s) = -1050*s**3 + 1655*s**2 - 863*s + 134. Let p(w) = -525*w**3 + 827*w**2 - 432*w + 66. Let y(z) = 5*p(z) - 3*t(z). If y(r) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Let u(a) be the third derivative of 1331*a**6/320 - 121*a**5/80 - 165*a**4/64 + 9*a**3/4 + 41*a**2. If u(t) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let w(z) = -z**3 + z**2 - z - 1. Let c(j) be the first derivative of -225*j**4/2 + 71*j**3 + 49*j**2 - 31*j - 3. Let r(l) = -c(l) - 5*w(l). Express the second largest root of r(o) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let n be 4*(-3)/6 + -12 + 1454/9. Express the second largest root of -n*x**2 + 32 - 8008/9*x**3 + 152*x = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Suppose 630*v**2 + 4368*v**3 + 58*v**2 + 360 - 1598*v - 430*v = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let i(j) be the third derivative of -27*j**6/2 - 5439*j**5/20 - 9959*j**4/6 + 1058*j**3 + 44*j**2 + 2. For i(d) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37", "dataset": "MATH"}
{"messages": [{"content": "If -818*h - 1341*h - 7104*h**2 - 7280*h**3 - 216 - 476*h + 439*h = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let r(g) be the third derivative of -103/2*g**5 + 70/3*g**6 - 45/2*g**3 + 0*g + 5*g**2 + 375/8*g**4 + 0. For r(k) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let x(w) be the second derivative of -336*w**5/5 + 1318*w**4/15 - 44*w**3/5 - 144*w**2/5 + 229*w. Find the value of n + m, where n/m is the second largest root of x(v) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let z(g) be the second derivative of -105*g**5/13 + 370*g**4/39 + 902*g**3/39 + 168*g**2/13 - 4*g + 11. Let z(r) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let q(x) = 125*x**3 - 6*x - 1225*x**3 - 65 + 690*x**2 + 78*x. Let r(v) = -550*v**3 + 345*v**2 + 36*v - 33. Let a(b) = 6*q(b) - 11*r(b). For the polynomial a(t), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For 1960*o**3 + 643*o**2 - 737 + 1772*o**2 + 990*o + 872 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let m(y) = -y. Let c(u) = 53*u**2 + 195*u**2 + 67*u**2 - 57*u + 12*u - 27 + 550*u**3. Let g(l) = -4*c(l) - 36*m(l). Find the value of n + m, where n/m is the second largest root of g(z) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let o(f) be the third derivative of -385*f**6/6 + 46*f**5 + 105*f**4/8 - 45*f**3/2 + 78*f**2. Express the second largest root of o(v) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let m = -43/644 - -81359/3220. Let m - 1862/5*a**2 + 8918/15*a**3 - 42/5*a = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 135/2*t + 250/3*t**2 - 375/2*t**3 - 30, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let g = -19 + 127. Suppose -4421*b**2 - 3539*b**3 - 461*b**3 + 821*b**2 - g - 1080*b = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -81/17*a - 600/17*a**2 - 273/17*a**3 + 54/17, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Suppose 3*c - 8446 = 5*l, 4*c = -2*l + 3*l + 11250. Suppose c*h**2 + 484*h + 1324*h**3 + 694*h + 154*h + 496*h**3 + 180 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let j(f) be the second derivative of -2079*f**5/20 + 1033*f**4/4 - 252*f**3 + 120*f**2 - 2*f + 266. Suppose j(i) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -1008/19*h - 1890/19*h**3 + 135/19 + 2427/19*h**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let a(x) = -245*x**3 - 70*x**2 + 81*x + 27. Let d(k) be the second derivative of -k**4/12 - 5*k. Let u(j) = 2*a(j) - 14*d(j). For u(i) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let o(u) = 2242*u**3 - 2467*u**2 + 893*u - 113. Let z(f) = -6727*f**3 + 7402*f**2 - 2679*f + 338. Let r(x) = 7*o(x) + 2*z(x). Let h(v) = 2240*v**3 - 2466*v**2 + 894*v - 114. Let y(g) = -7*h(g) + 6*r(g). For y(c) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let f(c) be the second derivative of -891*c**5/10 - 108*c**4 + 1013*c**3/3 - 210*c**2 + 55*c. Find the value of n + m, where n/m is the second largest root of f(g) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let h = -73 - -76. Find the value of n + m, where n/m is the second largest root of 198*p - 36*p**3 - 175*p**3 - 210*p**3 - 219*p**h + 54 - 96*p**2 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let y(r) = 6163*r**3 + 690*r**2 - 762*r - 135. Suppose 13 = 3*h + z, -z = -2*z - 2. Let n(l) = -12325*l**3 - 1380*l**2 + 1525*l + 270. Let b(d) = h*y(d) + 3*n(d). For b(c) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 2568*h**2 + 14*h + 4166*h**3 - 2*h + 356*h**3 - 108 + 6*h, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let w be (-48)/(-15)*5 - -20. Let 297/16*v - w*v**2 - 132*v**3 + 81/16 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let m(g) be the third derivative of 0*g + 25/4*g**6 + 27/2*g**3 - 15/4*g**5 + 0 - 45/4*g**4 - 4*g**2. Let m(v) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let 336/17*o + 556/17*o**2 - 180/17 - 840/17*o**3 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let w(b) be the third derivative of -49*b**6/6 + 28*b**5/5 + 33*b**4/8 - 9*b**3/2 + 80*b**2. Suppose w(z) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let c(l) be the first derivative of 261/2*l**2 + 108*l - 23 - 735/4*l**4 - 98*l**3. For c(g) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let l(d) be the third derivative of 117*d**6/80 + 211*d**5/280 - 71*d**4/28 - 24*d**3/7 - 52*d**2. Suppose l(i) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For 576/7 + 3468/7*x + 270*x**3 + 5727/7*x**2 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For -2400*q**3 - 1055*q + 30 + 299*q - 6 + 2340*q**2 + 57 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For -890/13*z + 6160/13*z**3 + 600/13 - 4330/13*z**2 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let n = 224448/11 + -20397. For the polynomial 1362/11*c**2 - 108/11 + 1365/11*c**3 + n*c, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let j(r) be the third derivative of -329*r**6/24 - 10763*r**5/60 + 16685*r**4/28 - 5076*r**3/7 + 5*r**2 + 2. Suppose j(v) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let a(z) = -2800*z**3 - 1804*z**2 + 201*z + 168. Let j(x) = 39200*x**3 + 25255*x**2 - 2815*x - 2350. Let t(g) = -85*a(g) - 6*j(g). If t(h) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let b(k) = -994*k**3 - 207*k**2 + 368*k - 67. Let n(h) = 993*h**3 + 206*h**2 - 366*h + 66. Let o(t) = -3*b(t) - 4*n(t). Express the second largest root of o(v) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let i(j) be the second derivative of -81/23*j**2 + 141/23*j**4 - 4*j - 45/23*j**3 + 168/23*j**5 + 0. Let i(b) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let o(m) = 505*m**3 + 55*m**2 - 355*m + 90. Let z(r) = 764*r**3 + 82*r**2 - 540*r + 128. Let p(l) = 763*l**3 + 82*l**2 - 539*l + 129. Let q(i) = 7*p(i) - 6*z(i). Let j(u) = 7*o(u) - 5*q(u). If j(d) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let b(i) be the third derivative of i**8/7 + 2*i**7/35 - 33*i**6/80 - 27*i**5/40 - i**4/12 + 9*i**2. Let t(z) be the second derivative of b(z). Let t(j) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "If 26455/6*k**3 - 1332 - 67303/6*k**2 + 7363*k = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let z(p) be the second derivative of 11*p + 0 - 320/3*p**4 - 75/2*p**3 + 90*p**2 + 385/4*p**5. For the polynomial z(i), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let v(q) = 2*q - 8. Let d be v(5). Express the second largest root of 1920/11*r**3 - 2016/11*r**d + 702/11*r - 81/11 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let s(z) = -562*z**3 - 280*z**2 + 45*z + 25. Let y(a) = -a**3 + a**2 - 1. Let g(q) = -s(q) + 2*y(q). Express the second largest root of g(r) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let u(x) be the second derivative of -3*x + 9*x**3 - 66*x**5 - 309/4*x**4 + 0 + 81/2*x**2. Let u(j) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let o(c) = -653*c**3 - 782*c**2 - 294*c - 33. Let x(p) = p**3 - p**2 - p - 1. Suppose 0 = 6*b - 11 - 7. Let r(u) = b*x(u) + o(u). For the polynomial r(d), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let u(s) be the first derivative of 19855*s**4/18 + 1729*s**3/9 - 190*s**2 - 57*s - 140. Express the second largest root of u(l) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let y(c) = -265*c**3 + 183*c**2 + 41*c - 27. Let u(v) = -268*v**3 + 183*v**2 + 40*v - 27. Let z(m) = -5*u(m) + 4*y(m). For z(i) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let x(l) be the second derivative of 3861*l**5/32 + 4975*l**4/16 + 4435*l**3/16 + 225*l**2/2 - 366*l. For x(v) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let a(x) = 5007*x**3 + 5993*x**2 + 2257*x + 263. Suppose -y + 11 = 5*i, 3*y + 4 = -2*i - 2. Let u(l) = 2503*l**3 + 2997*l**2 + 1128*l + 132. Let w(z) = i*a(z) - 7*u(z). Find the value of n + m, where n/m is the second largest root of w(v) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let u(v) be the third derivative of 63*v**6/80 + 97*v**5/100 - 97*v**4/80 - 3*v**3 + 133*v**2. Suppose u(z) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Let o(q) be the first derivative of -1456*q**4/9 - 2104*q**3/27 + 140*q**2/3 + 32*q + 58. Suppose o(r) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let g(h) be the second derivative of 35*h**6/4 + 33*h**5/4 - 9*h**4 - 27*h**3/2 + 5*h**2 - 3*h. Let w(n) be the first derivative of g(n). For w(a) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 1049*p + 681*p**3 + 55*p**3 + 58*p + 2944*p**2 + 1487*p**3 + 126 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose -2*l + 473 - 464 = -5*w, -l - 3 = 5*w. Suppose -72/5 - 704/3*f**3 - 1464/5*f**l - 576/5*f = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 3584/15*b**3 - 4352/15*b**2 + 536/5*b - 12 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let p be (-8)/6*((-9)/(-2))/(-3). Let -662*b**p + 81 - 246*b + 68*b**2 + 1419*b**3 + 261*b**3 + 3*b = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let w(t) be the first derivative of 196*t**4 - 81*t**3 - 72*t**3 - 54*t**2 + 27*t**3 - 12 + 54*t. For the polynomial w(u), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 362*m - 284*m - 1980*m**3 - 883*m**2 + 252 - 2251*m**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let v(h) be the first derivative of 77*h**5/5 - 129*h**4/13 - 54*h**3/13 + 54*h**2/13 - 14*h - 1. Let o(w) be the first derivative of v(w). Express the second largest root of o(r) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let z(b) be the first derivative of 18 + 365*b**3 + 180*b**2 - 16 - 135*b - 550*b**4 - 15. Express the second largest root of z(j) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let l be (-27)/(-8 - 78/(-18)). If 168*o**3 - 108/11*o + 981/11*o**2 - l = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let y(p) = 1 - p. Let h(f) = 438*f**3 + 196*f**2 - 84*f - 33. Let q(n) = h(n) - 6*y(n). Let x(s) = s**3 - s + 1. Let a(w) = q(w) + 3*x(w). Express the second largest root of a(r) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Suppose -3*v + r + 2620 = 0, -117*v + 115*v + 1756 = 4*r. For the polynomial 1368/7 - v*q**2 + 798*q - 30096/7*q**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let h be ((-3280)/(-20) - (2 + 0))*(-1)/(-14). If -75*m**3 + 27*m - h + 225/7*m**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let t(g) = 5078*g**3 + 825*g**2 - 1003*g + 104. Let x(o) = 15235*o**3 + 2475*o**2 - 3008*o + 313. Let q(p) = -11*t(p) + 4*x(p). Express the second largest root of q(l) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Let k(q) be the first derivative of -10544/21*q**3 - 720/7*q + 21 - 2496/7*q**2 - 1760/7*q**4. Let k(n) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let w(y) be the third derivative of -88*y**6/15 + 106*y**5/25 + 57*y**4/10 - 18*y**3/5 + 8*y**2. Find the value of n + m, where n/m is the second largest root of w(h) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Let i(s) = 15945*s**3 - 15942*s**2 - 3333*s + 909. Let y(a) = -3986*a**3 + 3985*a**2 + 833*a - 228. Let m(j) = -4*i(j) - 15*y(j). For the polynomial m(x), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Let s = -3918 - -3920. For 1485/7*t + 2600/7*t**3 + 3655/7*t**s + 180/7 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 322*y + 3083*y - 2725*y**3 + 630 - 2995*y**3 + 2455*y**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Suppose -2 + 14 = 3*m + 2*j, -2 = 2*m - 2*j. Express the second largest root of -414*a**m + 43 + 9 + 29 + 297*a - 1680*a**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For -134*s - 146*s + 477*s + 397*s + 1050*s**3 + 81 + 1395*s**2 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -1548*y + 1568*y**3 + 119*y**2 + 244*y**2 + 22*y**2 + 360 + 595*y**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let x(g) be the third derivative of 63/40*g**5 + 11/8*g**6 - 27/20*g**3 + 0*g + 0 + 4*g**2 - 27/40*g**4. For the polynomial x(o), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let z be -4 + (12/3 - 10) + 13. For the polynomial -602*n**2 + 1911/8*n + 504*n**z - 63/2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let m(l) be the third derivative of 35/32*l**6 - 9/4*l**3 + 12*l**2 + 61/32*l**5 + 0*l - 3/64*l**4 + 0. If m(h) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Let w(c) be the second derivative of 2002/25*c**5 + 329/12*c**4 - 126/5*c**2 - 6*c - 357/10*c**3 + 0. For the polynomial w(g), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let z(l) be the second derivative of -26*l**5 - 7*l + 1406/21*l**4 - 444/7*l**3 + 0 + 180/7*l**2. Find the value of n + m, where n/m is the second largest root of z(h) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let y(r) = 6191*r**3 - 702*r**2 - 992*r + 189. Let p(m) = -18572*m**3 + 2108*m**2 + 2976*m - 568. Let s(g) = -3*p(g) - 8*y(g). If s(j) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Let q(h) be the third derivative of 175*h**6/6 + 175*h**5/8 - 105*h**4/8 - 315*h**3/16 + 8*h**2. Let q(j) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let t(z) be the third derivative of 55*z**8/256 + 37*z**7/448 - 21*z**6/64 - 27*z**5/64 + 7*z**4/24 + 13*z**2. Let m(u) be the second derivative of t(u). Express the second largest root of m(f) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let h(g) = -553*g**3 + 645*g**2 - 234*g + 27. Let k(n) be the third derivative of -277*n**6/60 + 43*n**5/4 - 39*n**4/4 + 9*n**3/2 - 14*n**2. Let o(w) = -4*h(w) + 3*k(w). Suppose o(p) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -216/5 + 216*d**3 - 693/5*d + 93/5*d**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -113 + 41*n + 401*n**3 - 104*n**2 + 95 - 86*n**3 + 78 - 192*n = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let p(g) be the first derivative of -819*g**4/4 + 265*g**3/3 + 76*g**2 - 48*g + 95. If p(v) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let v be 6/34 - (-39246)/136. Express the second largest root of -1053/8*f**2 + 81/8 - v*f**3 + 81/4*f = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Suppose -2*n = -4*g + 24, -3*g = -2*g + n. Let r(k) = 499*k**3 + 707*k**2 - 192*k - 100. Let m(d) = -997*d**3 - 1414*d**2 + 385*d + 199. Let y(x) = g*m(x) + 7*r(x). If y(h) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let y(n) be the first derivative of -13 - 792/13*n + 1089/13*n**2 + 4774/39*n**3 - 2695/13*n**4. For the polynomial y(s), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose p + 72 = 5*y, 3*p - 42 = -3*y + 4*p. For 1 + 4 + 700*n**3 + 330*n**2 - 144*n - 44 - y = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let t(r) be the first derivative of 77*r**7/30 - 49*r**6/30 - 33*r**5/10 + 9*r**4/2 - 20*r**3/3 - 3. Let w(b) be the third derivative of t(b). Let w(o) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Suppose -9 = 2*x - 5*x. For the polynomial 70*r - 7*r**3 + 246*r**3 + 492*r**2 - 75 + 121*r**x, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Suppose -252/17*z**2 + 81/17 - 27*z + 2940/17*z**3 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let a(t) be the first derivative of 25*t**7/154 - 5*t**6/22 - 9*t**5/88 + 27*t**4/88 + 11*t**3/3 + 11. Let h(j) be the third derivative of a(j). Express the second largest root of h(y) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let q(b) be the third derivative of 77*b**9/37440 + 29*b**8/4160 + 15*b**7/1456 + 9*b**6/1040 - 3*b**5/20 + 14*b**2. Let i(a) be the third derivative of q(a). If i(t) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let a(m) be the first derivative of -384*m**4/13 - 320*m**3/13 + 108*m**2/13 + 135*m/13 + 76. If a(j) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let o = -3418 + 27425/8. For the polynomial 525/4*g**3 - 27*g + o - 495/8*g**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "If 108/23 - 1245/23*i**2 - 297/23*i + 3150/23*i**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let n(p) be the third derivative of -484*p**7/105 - 11*p**6/6 + 21*p**5/5 + 9*p**4/2 + p**3/3 - 15*p**2. Let h(z) be the first derivative of n(z). Find the value of n + m, where n/m is the second largest root of h(k) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let z be 227700/368*80/78. For the polynomial -270/13 - 2610/13*i - z*i**2 - 8470/13*i**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let a(c) be the first derivative of -1755/2*c**4 - 216*c + 331*c**3 + 369*c**2 + 33. Express the second largest root of a(t) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let i(o) be the third derivative of 275/32*o**5 - 225/16*o**3 + 0 + 125/24*o**6 + 0*o - 75/32*o**4 + 2*o**2. For the polynomial i(f), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let y(w) = w**2 + 17*w + 5. Let f be y(-17). Let o(n) = 4475*n**3 - 1589*n**2 - 648*n + 216. Let s(c) = 2237*c**3 - 795*c**2 - 324*c + 108. Let q(x) = f*s(x) - 3*o(x). Express the second largest root of q(m) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let x(m) be the third derivative of -75/56*m**5 - 45/28*m**4 - 25/56*m**6 - 7*m**2 + 0*m + 0 - 27/28*m**3. Find the value of n + m, where n/m is the second largest root of x(b) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 14080/7*t**3 + 6570/7*t - 17040/7*t**2 - 810/7 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let y(x) = 4704*x**3 - 4814*x**2 + 1566*x - 175. Let h(f) = 784*f**3 - 802*f**2 + 261*f - 29. Let k(z) = 39*h(z) - 6*y(z). For k(c) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let -200/3*w**3 + 48/7 + 100/21*w**2 + 212/7*w = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let o be (-1)/(0 + 1 - 2)*167. For 283*a**3 + 273*a**2 + o*a**2 - 146*a + 167*a**3 - 168 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let i(u) be the third derivative of 119*u**6/120 + 229*u**5/60 - 3*u**4/2 - 6*u**3 - 203*u**2. For i(a) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Suppose 700/11*l**3 + 72/11*l + 100*l**2 - 288/11 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Let k(u) be the first derivative of 625*u**4/2 + 5375*u**3/3 - 975*u**2 - 1035*u - 75. Suppose k(c) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let v(o) be the first derivative of -825*o**4/28 - 130*o**3/7 + 351*o**2/14 + 108*o/7 - 45. For v(j) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let u(j) be the second derivative of -55*j**5/3 - 1210*j**4/27 - 187*j**3/18 + 77*j**2/2 + 93*j. Express the second largest root of u(z) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let i(c) = -c**2 - 1. Let a(p) = -1982*p**3 - 2020*p**2 - 666*p - 76. Let t(h) = a(h) - 6*i(h). Let n(z) = 7929*z**3 + 8056*z**2 + 2664*z + 279. Let x(s) = 2*n(s) + 9*t(s). Let x(y) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 2800/13*b - 1100/13*b**3 - 480/13 - 3670/13*b**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let i(n) = -1003*n**3 + 300*n**2 + 93*n - 24. Let l = -15 - -21. Let a(m) = 4013*m**3 - 1200*m**2 - 373*m + 95. Let r(f) = l*a(f) + 26*i(f). For the polynomial r(y), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let q = 1076 - 141. Suppose 1377*i**2 + 3213/5*i + q*i**3 + 459/5 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let r(j) be the second derivative of -484*j**5/5 + 121*j**4/2 + 128*j**3/3 - 48*j**2 + 33*j. For the polynomial r(v), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let i(b) = -13*b**3 - 13*b**2 - 27*b + 2. Let p be i(-2). Suppose -1179/5*x**2 - 168*x**3 - 81/5 - p*x = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let h = 1247215/8 - 155600. For the polynomial 63/2 - 7623/8*n**3 - h*n + 3773/4*n**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let v = -9097645/14 + 36393667/56. For -v*h**2 + 135/8*h + 81/8 - 735/8*h**3 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let x(h) be the second derivative of 121*h**8/1344 + 121*h**7/840 - h**6/16 - 9*h**5/40 - 5*h**4/2 - 7*h. Let r(z) be the third derivative of x(z). Let r(o) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let w(x) = -x**2 - 20*x - 96. Let b be w(-11). For 520/9*g**2 - 16/3*g - 400/9*g**b - 8 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Suppose -8*l + 11*l - 10890 = 0. For the polynomial -888*g**2 - 2233*g**2 - 892*g**2 - l*g**3 - 1053*g - 108 + 614*g**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For 7056/11*c**3 + 1750/11*c**2 - 2506/11*c - 840/11 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let w(f) = 25167*f**3 + 2607*f**2 - 11169*f + 2271. Let j(m) = 1573*m**3 + 163*m**2 - 698*m + 142. Let q(a) = 33*j(a) - 2*w(a). Suppose q(h) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let m(a) = -440*a**3 + 549*a**2 - 213*a + 30. Let t(h) = -880*h**3 + 1094*h**2 - 427*h + 59. Let v(l) = 1760*l**3 - 2187*l**2 + 854*l - 118. Let d(q) = 9*t(q) + 4*v(q). Let x(p) = -6*d(p) + 10*m(p). Suppose x(n) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let p(k) be the first derivative of -183/20*k**3 - 21/2*k**4 - 7 + 27/10*k**2 + 81/20*k. For the polynomial p(n), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let f(p) = 4666*p**3 + 16921*p**2 + 14865*p + 3840. Let t(s) = 2332*s**3 + 8460*s**2 + 7432*s + 1920. Let o(w) = -4*f(w) + 7*t(w). Let o(q) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Suppose 32*x = 35*x - 93. If -5 - 3*j - 5*j - j + 346*j**2 - 385*j**3 - x = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -130*p**2 + 117*p**2 + 1440*p**3 + 948*p + 144 + 864*p**2 + 1193*p**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let b(i) be the first derivative of -81/7*i + 150/7*i**4 + 165/7*i**3 + 12 - 27/7*i**2. For the polynomial b(v), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Suppose 5*k - 8*k = -36. Suppose -24 + 34*p - 75*p**3 - k + 5*p - 485*p**3 + 362*p**2 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let x(b) be the second derivative of 0 - 105*b**3 + 451/3*b**4 + 22*b - 847/10*b**5 + 36*b**2. For the polynomial x(h), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Suppose -4640 = -45*v + 16*v. If 216/19 - v*x**3 - 276/19*x**2 + 900/19*x = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let g(h) be the first derivative of 2475*h**4/7 - 12970*h**3/21 + 2750*h**2/7 - 750*h/7 + 40. For the polynomial g(t), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let s(k) be the third derivative of 221*k**6/64 + 2779*k**5/320 + 411*k**4/128 - 135*k**3/16 + 36*k**2. Express the second largest root of s(t) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Suppose 3*z = 7*z - 324. Let 723*f**2 + 379*f + z + 735*f**3 - 71*f + 205*f + 348*f**2 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of -318*o - 841*o**2 + 2308*o**3 + 34*o**2 + 905*o**3 + 144 - 303*o + 21*o = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Let 294*n**2 + 864*n**2 + 216*n - 69*n**2 - 81 - 2904*n**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let l(g) be the second derivative of 462/5*g**5 + 81/2*g**2 - 135/4*g**4 + 0 + 8*g - 54*g**3. If l(d) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Suppose -5*t = q - 590, q + 3*t = 196 + 386. For the polynomial 513/7 - q*i**2 - 7600/7*i**3 + 171*i, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Suppose 2083*w**2 - 2950*w**2 + 166*w - 174*w**3 - 970*w**3 + 120 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let o(j) be the third derivative of 539*j**6/120 + 49*j**5/4 + 41*j**4/3 + 8*j**3 - 51*j**2. Suppose o(r) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 261*y**3 + 1743*y**2 + 255*y**3 - 122*y**3 - 270 + 441*y + 502*y**3 + 94*y**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Let x(u) = -u**3 + u**2 + 3*u - 4. Let d(g) = 2*g**3 - 2*g**2 - 5*g + 7. Let h(l) = -3*d(l) - 5*x(l). Let z(o) = 996*o**3 + 1579*o**2 + 810*o + 131. Let f(k) = -4*h(k) + z(k). Let f(t) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of -45*p + 180/7 - 2990/7*p**2 + 6800/7*p**3 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let f be 6/5 - 839/(-5). Suppose -534*m**2 + 2860*m**3 + 72 + 59*m**2 - 314*m**2 - 210*m - f*m**2 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let z(k) be the third derivative of -55*k**6/3 - 183*k**5/4 - 45*k**4 - 45*k**3/2 - 9*k**2 + 4*k. If z(u) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let c(a) be the first derivative of 110*a**4 - 359*a**3 - 509*a**2/2 + 210*a - 45. Suppose c(d) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let f(s) = -s**3 + s**2 + s + 1. Let d(g) = 1675*g**3 - 365*g**2 - 1020*g + 380. Suppose 1 - 3 = 2*z - 2*l, 0 = 4*z + 2*l + 28. Let n(w) = z*f(w) + d(w). For the polynomial n(y), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let n(o) be the third derivative of -231*o**6/128 + 299*o**5/160 + 117*o**4/128 - 9*o**3/8 - 26*o**2 - 2*o. If n(v) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Let c(u) be the first derivative of 252/5*u - 399/10*u**2 + 21 - 1358/15*u**3 + 441/4*u**4. Express the second largest root of c(a) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "If -98*q + 220*q**3 - 41 + 634*q**2 - 55 - 78*q**2 + 282*q = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Let z = 107869/13290 + -22/1329. Find the value of n + m, where n/m is the second largest root of -297/10*k + 1617/10*k**3 - 441/10*k**2 + z = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let r(q) be the third derivative of -11*q**8/350 + 4*q**7/175 + 33*q**6/800 - 27*q**5/400 + 7*q**4/12 - 15*q**2. Let v(j) be the second derivative of r(j). For v(n) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let x(l) be the second derivative of 56*l**6/25 + 132*l**5/25 + 207*l**4/40 + 27*l**3/10 - 3*l**2/2 + 5*l. Let z(k) be the first derivative of x(k). Express the second largest root of z(m) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "If 1506/11*p - 2091/11*p**2 + 840/11*p**3 - 315/11 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Let t be (2/8 + 4/(-4))*88/(-22). Suppose 81/5 - 462*z**t + 2313/5*z**2 - 756/5*z = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose -327 = -5*t - 57. Let -70*u**2 - 7*u**2 + 2420*u**3 + t - 216*u - 517*u**2 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Suppose -5*b + 972 = g - 468, 4*b + 12 = 0. For -g*m**2 + 181*m - 52 + 160 - 4950*m**3 + 33*m + 155*m = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let h be -9*(86/(-66) + (-16)/44). For 1525*x**2 - 1750*x**3 + h*x + 15 - 110 - 33 - 52 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let v(t) be the third derivative of 0 + 363/160*t**5 + 0*t + 121/64*t**6 - t**2 - 45/64*t**4 - 27/16*t**3. For v(r) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let z = 787073/2080 - 3661/416. Let -1107/5*s**2 + 243/5*s + 162/5 - z*s**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let s(a) be the third derivative of 0 - 15/4*a**3 + 385/72*a**6 + 0*a - 10*a**2 + 35/4*a**4 - 257/24*a**5. Suppose s(w) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let u(l) = -232*l**2 + 1627*l - 19. Let v be u(7). If 162/19*s + 459/19*s**v - 840/19*s**3 - 81/19 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let u(j) be the second derivative of 33*j**5/14 - 9*j**4/4 + 9*j**3/14 - 11*j - 3. Express the second largest root of u(f) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let k(p) be the first derivative of -385*p**4/4 - 142*p**3 + 1051*p**2/2 + 420*p + 66. For the polynomial k(t), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let m be (2 - -2 - 2) + 586. Express the second largest root of -991*g**3 - 108 + 266*g + 11*g**3 + m*g**2 - 86*g = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let o(y) = 1589*y**3 - 3314*y**2 + 1759*y - 249. Let p(j) = 794*j**3 - 1657*j**2 + 879*j - 126. Let s(x) = 4*o(x) - 10*p(x). For the polynomial s(b), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let r(z) = 3520*z**3 + 4385*z**2 + 1721*z + 216. Let y(n) = 1760*n**3 + 2192*n**2 + 860*n + 108. Let x(h) = 3*h + 8. Let i be x(-4). Let t(l) = i*r(l) + 7*y(l). If t(w) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let u(b) be the third derivative of 27/2*b**3 + 0 + 12*b**2 + 45/2*b**4 + 25/4*b**6 + 0*b + 75/4*b**5. For the polynomial u(v), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let w(d) = -4 - 4*d - d**3 + d**2 + 3*d - 2*d**2 + 5. Let o(a) = 1161*a**3 - 507*a**2 - 237*a + 75. Let f(b) = -o(b) - 6*w(b). For the polynomial f(l), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "For 122*u**2 + 3*u + 90 + 924*u**3 - 70*u - 365*u = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let b = 476 - -208. Let 38 + 56 - b*r**2 - 324*r + 14 + 1540*r**3 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let b(j) = -j**3 + 14*j**2 - 14*j + 15. Let s be b(13). Suppose 153*l**s - 84*l**3 - 27 + 57*l**2 + 484*l**3 - 74*l + 11*l = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -544*a + 165*a**2 - 192 + 522*a**2 - 27*a**2 + 1300*a**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let c(s) = 3504*s**3 + 3320*s**2 + 1060*s + 108. Let a(u) = -u**3 - u**2 + u. Let r(f) = 16*a(f) - c(f). Find the value of n + m, where n/m is the second largest root of r(v) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let g(a) be the first derivative of -3 + 1615/4*a**2 + 102*a + 6307/9*a**3 + 10829/24*a**4. For the polynomial g(w), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let n(j) be the second derivative of 27*j**5/8 + 257*j**4/56 - 2*j**3 - 36*j**2/7 + 66*j. If n(t) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let x = -55221/5 - -11097. For the polynomial 2156/3*l**3 - 198/5 + 2002/5*l**2 - x*l, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let l be ((-40)/(-150) + (-613)/780)/(2/(-24)). Express the second largest root of 189/13*g + l - 441/13*g**2 - 1029/13*g**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let q(g) = -520*g**3 - 523*g**2 + 360*g + 107. Let i(m) = -1040*m**3 - 1046*m**2 + 719*m + 215. Let w(h) = 4*i(h) - 10*q(h). Suppose w(v) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let p = 2975461/9240 + 289/840. For 54/11*k - 324/11 + p*k**2 - 336*k**3 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "If 1250*d**2 + 1004*d**3 - 360 - 215*d**3 - 465*d + 86*d**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let x(j) be the second derivative of -231*j**5/52 + 323*j**4/26 - 349*j**3/26 + 90*j**2/13 + 13*j + 1. Find the value of n + m, where n/m is the second largest root of x(k) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let a(v) be the second derivative of -5*v**7/27 + 131*v**6/216 - 5*v**5/6 + 5*v**4/8 + v**3 - 11*v. Let q(w) be the second derivative of a(w). Express the second largest root of q(m) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let q(g) be the third derivative of -77*g**6/4 - 709*g**5/12 - 135*g**4/2 - 75*g**3/2 - 94*g**2. Let q(y) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let s be 4 - 4 - (9 + -11). For the polynomial 432/7 + 5100/7*d**s - 3000/7*d**3 - 2700/7*d, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let x(j) be the third derivative of j**9/288 + 37*j**8/24640 - 3*j**7/440 - 9*j**6/880 - j**5/12 + 3*j**2. Let t(d) be the third derivative of x(d). Express the second largest root of t(u) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 2264*a**2 - 828*a - 1284*a**3 - 396*a**3 - 3888 + 3978, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let v(z) = z**2 + 1. Let j(o) = -o**3 + 2*o + 2. Let l be j(0). Let q(f) = 847*f**3 + 443*f**2 - 51*f - 33. Let h(s) = l*q(s) - 6*v(s). Express the second largest root of h(c) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let m = -782 + 950. For the polynomial 603/11*w**2 - 81/11 - 270/11*w + m*w**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let c = 60 - 58. For -244*b**3 - 398*b**2 + c + 70 + 234*b - 1016*b**3 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let q(l) = 1200*l**3 - 214*l**2 - 410*l + 81. Let o(b) = -400*b**3 + 71*b**2 + 136*b - 27. Let h(i) = -11*o(i) - 4*q(i). If h(u) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let k(n) = -4166*n**3 - 1686*n**2 + 3015*n - 681. Let z(o) = -4165*o**3 - 1685*o**2 + 3015*o - 680. Let m(j) = 5*k(j) - 6*z(j). If m(d) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "If 102*o**3 + 2388*o**2 - 108 + 2626*o**3 + 752*o**3 + 328*o**3 + 72*o = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let q = 22684/75 + -9244/75. Express the second largest root of q*d**2 + 567/10*d - 126/5 - 2016/5*d**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let j(n) be the first derivative of -65*n**7/294 + 10*n**6/63 + 39*n**5/70 - 6*n**4/7 - 14*n**3/3 - 18. Let d(g) be the third derivative of j(g). Express the second largest root of d(s) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "For 675/7 + 1125*k + 4000*k**3 + 26700/7*k**2 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let 153/8*q - 189/8 + 165*q**2 + 225/2*q**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Suppose 1401/8*t + 180*t**3 - 1311/4*t**2 - 45/2 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let a be (9747/(-6840))/((1/4)/(-1)). Suppose 27/10 - 63/5*x + 21*x**3 + a*x**2 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let g(j) be the second derivative of 441/32*j**5 - 369/16*j**3 - 81/4*j**2 + 13*j + 0 + 21/16*j**4. If g(u) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let p(t) = 985*t**3 - 2685*t**2 + 1530*t - 245. Let w(j) = -493*j**3 + 1343*j**2 - 766*j + 122. Let n(q) = 2*p(q) + 5*w(q). If n(y) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let b(o) = 849*o**3 - 97*o**2 - 133*o + 29. Let l(i) = -56*i**2 - 1512*i**3 + 346*i**2 - 1036*i**3 - 34 + 398*i - 54. Let m(j) = 14*b(j) + 4*l(j). Let m(f) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Suppose -3*r = -4*p - 33, 4*r + 246*p - 247*p - 18 = 0. Let 2475/17*y**2 + 2541/17*y**r + 783/17*y + 81/17 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "If -378*w + 5434*w**3 + 19 + 239*w**2 - 869*w**2 + 35 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Let l(i) be the third derivative of -224*i**6/15 - 1376*i**5/15 + 49*i**4/2 + 150*i**3 + 214*i**2. If l(c) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let p(d) be the third derivative of 9*d**8/35 + 8*d**7/21 - 27*d**6/80 - 9*d**5/8 - 11*d**4/24 + 5*d**2. Let t(w) be the second derivative of p(w). Express the second largest root of t(l) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let d be -2*5/30*52272/(-128). If 81/8 - 513/16*n - d*n**2 + 6897/16*n**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let m(t) be the first derivative of -135/2*t**2 + 2695/4*t**4 - 525*t**3 + 13 + 135*t. Express the second largest root of m(s) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let y(f) be the first derivative of 640*f**4 + 3328*f**3/3 + 684*f**2 + 180*f + 39. Suppose y(j) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let d(m) = -298*m**3 - 1842*m**2 - 475*m + 317. Let i(k) = k**3 - k**2 - 2*k + 1. Let y(f) = -3*d(f) + 6*i(f). Find the value of n + m, where n/m is the second largest root of y(w) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let o(z) be the third derivative of 4*z**9/135 - 4*z**8/105 - z**7/20 + 3*z**6/20 - z**5/20 + 4*z**2. Let y(i) be the third derivative of o(i). Suppose y(g) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let z(x) = -x**3 - 9*x**2 - 6*x + 11. Let j be z(-8). Let p(a) = -1603*a**3 + 117*a**2 + 465*a - 111. Let n(h) = 3205*h**3 - 235*h**2 - 931*h + 221. Let c(o) = j*p(o) - 3*n(o). For the polynomial c(m), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose -66 - 451/2*m + 1045/6*m**2 + 1925/3*m**3 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -1589*u**3 + 146 + 1960*u**2 + 364*u**3 - 1035*u + 34, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Suppose 122 + 704*y**3 + 2416*y**3 - 176 - 3616*y**2 + 216 - 316*y + 174 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose 15 = 6*q - q. If 6 - 1410*g**2 + 3532*g**3 - 732*g**q + 129 - 48*g - 177*g = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let a(g) be the first derivative of -5980*g**4/7 + 1242*g**3/7 + 3105*g**2/14 - 621*g/7 - 48. Suppose a(d) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let r(l) be the second derivative of 238*l**5/9 - 292*l**4/9 - 2788*l**3/27 - 176*l**2/3 + l - 6. Suppose r(h) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let w(h) = 362*h - 3256. Let d be w(9). If -5640/11*l**d + 1926/11*l + 5400/11*l**3 - 216/11 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let g(x) = 1591*x**3 + 1881*x**2 + 715*x + 103. Let b(m) = -795*m**3 - 940*m**2 - 359*m - 51. Let r(s) = -7*b(s) - 3*g(s). For r(n) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let b(d) = 539*d**3 + 312*d**2 - 27*d - 27. Let t(r) = -1078*r**3 - 625*r**2 + 54*r + 54. Suppose 0 = -3*h - 7 - 2, 37 = 5*w - 4*h. Let o(a) = w*b(a) + 3*t(a). Suppose o(j) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let m(r) be the third derivative of 55*r**9/1512 + r**8/192 - r**7/8 - 3*r**6/16 - r**5/20 + 4*r**2. Let n(l) be the third derivative of m(l). Let n(x) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let u(w) be the second derivative of -429*w**5/64 - 131*w**4/16 + 3*w**3/32 + 27*w**2/8 + 44*w. For the polynomial u(s), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let y(c) be the third derivative of -49*c**6/6 + 77*c**5/5 - 93*c**4/8 + 9*c**3/2 - 6*c**2 - 5*c. For y(p) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let z(d) be the third derivative of -11*d**8/192 - 13*d**7/840 + 13*d**6/80 + 9*d**5/40 + d**4/8 - 24*d**2. Let u(c) be the second derivative of z(c). For the polynomial u(b), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let f = -1170 - -1173. Find the value of n + m, where n/m is the second largest root of -1960/3*p**f + 63/2 + 721*p**2 - 525/2*p = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Suppose 280 = 5*v + 5*h, -v + 0*h = 5*h - 64. Express the second largest root of -558/5*i - 798/5*i**2 + v + 294*i**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let m(t) be the first derivative of 715*t**4/4 - 214*t**3 - 32*t**2 + 96*t + 104. Express the second largest root of m(j) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let z(n) be the third derivative of -12/5*n**4 + 0 - 6/5*n**5 + 616/225*n**6 + 0*n + 12/5*n**3 + 5*n**2. Find the value of n + m, where n/m is the second largest root of z(q) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let x(k) be the first derivative of -5525*k**4/4 - 880*k**3 + 855*k**2/2 + 270*k - 4. For the polynomial x(y), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let d(r) be the first derivative of -88*r**7/105 - 8*r**6/15 + 33*r**5/40 + 9*r**4/8 + 4*r**3/3 + 29. Let m(j) be the third derivative of d(j). Let m(n) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Suppose -81/20 + 27/5*m - 273/2*m**3 + 1359/20*m**2 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let t(d) = -d**2 + 2*d + 17. Let r be t(-3). Let 550*b**3 + 297/8 - 165/4*b**r - 1287/8*b = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let f(h) be the third derivative of -11*h**8/448 - h**7/56 + 33*h**6/400 + 27*h**5/200 + 7*h**4/24 + 9*h**2. Let o(r) be the second derivative of f(r). Let o(p) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let g(z) be the first derivative of 480*z**4/7 - 992*z**3/7 + 675*z**2/7 - 27*z - 245. For the polynomial g(q), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 245/4*q**2 + 105/2 - 1050*q**3 + 2303/8*q, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For -420/17 + 1784/17*i**2 + 960/17*i**3 + 316/17*i = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Let w(j) be the second derivative of 1716*j**5/95 - 525*j**4/76 - 63*j**3/19 + 81*j**2/38 + 205*j. Express the second largest root of w(l) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let a(i) be the first derivative of 175*i**4 - 174*i**2 - 180*i - 16 + 340/3*i**3. Let a(b) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let n(c) be the first derivative of 880/17*c**4 + 522/17*c**2 - 108/17*c - 1 - 1112/17*c**3. For the polynomial n(k), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let g(j) = -3510*j**3 + 1311*j**2 + 351*j - 102. Let b(n) = -3510*n**3 + 1312*n**2 + 351*n - 103. Let o(v) = 6*b(v) - 5*g(v). For the polynomial o(y), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let f be 10/(35/33150*5). For the polynomial -1760*i**3 + f*i**2 + 540/7 - 4680/7*i, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let y = -24809/85 - -27209/85. Suppose 4950/17*l**3 - 7510/17*l**2 - y + 3440/17*l = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose 6 + 11 = 41*o - 65. Find the value of n + m, where n/m is the second largest root of -7920/13*u**3 + 81*u - 243/13 + 1566/13*u**o = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let a(f) be the second derivative of -165*f**8/1904 - 69*f**7/476 + 9*f**6/170 + 81*f**5/340 + 7*f**4/12 - f. Let h(c) be the third derivative of a(c). Suppose h(b) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let h(t) be the first derivative of -242*t**3 + 45*t**2 - 3 + 54*t - 605/2*t**4. Let h(l) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let p(t) = -3009*t**3 + 1413*t**2 + 138*t - 78. Let l(d) = 6016*d**3 - 2826*d**2 - 275*d + 157. Let h(i) = 3*l(i) + 5*p(i). Express the second largest root of h(f) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let w be ((-204)/15)/(8/(-80)). Express the second largest root of -960*l**2 - w*l - 120 - 27*l + 93 - 1100*l**3 - 116*l = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let g(n) be the third derivative of 0*n - 847/460*n**6 + 0 + 63/92*n**4 + 7*n**2 - 363/230*n**5 + 27/23*n**3. If g(i) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let c(x) = x**2 - x - 1. Let j(h) = -h - 8. Let v be j(-6). Let k(n) = -990*n**3 - 458*n**2 + 60*n + 27. Let u(o) = v*k(o) + 18*c(o). For the polynomial u(d), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 1353/5*v**2 - 363*v**3 + 306*v - 648/5, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let i(k) be the second derivative of -693*k**5/10 + 331*k**4/4 + 153*k**3/2 - 135*k**2 + 69*k. Suppose i(w) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -27*l + 75*l**3 + 225/13*l**2 - 81/13, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let y(g) be the third derivative of 18/13*g**3 + 511/260*g**5 + 0 + 0*g - 9/13*g**6 - 26*g**2 - 237/104*g**4. If y(j) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose -2443*a**2 - 341*a**2 - 9*a + 76*a**2 + 2080*a**3 + 504 + 45*a = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 352*s**3 - 644/9*s**2 - 196/3*s + 16 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Suppose 5*w + 7*h + 34 = 0, 210 = -4*h + 182. For the polynomial -8208/5*r**2 + 18624*r**w + 1296/5 - 24640*r**4 - 6912/5*r, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let o(c) = -20020*c**4 + 23214*c**3 + 16156*c**2 - 1571*c - 1129. Let l(k) = 20020*k**4 - 23214*k**3 - 16158*k**2 + 1572*k + 1128. Let p(y) = 5*l(y) + 6*o(y). If p(t) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Suppose -44055/7*s**2 + 3078/7 - 141933/7*s**3 + 10557/7*s + 35937/7*s**4 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let a(r) be the second derivative of -25*r**9/126 - 75*r**8/448 + 9*r**7/7 - 9*r**6/80 - 81*r**5/20 + 77*r**4/4 - r**3/3 - 2*r + 1. Let k(c) be the third derivative of a(c). For the polynomial k(y), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let h(g) = g**2 + 2343*g - 88057. Let y be h(37). If -18981/8*b + 999 + 32375*b**y - 121545/8*b**2 + 50875/2*b**4 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let l(b) = -b**3 + b**2. Let o = -140 + 141. Let n(d) = 8800*d**4 - 105*d**3 - 1987*d**2 + 9*d + 108. Let g(w) = o*n(w) - 5*l(w). Express the second largest root of g(q) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let p(v) be the second derivative of 8*v**8 + 492*v**7/35 + 81*v**6/20 - 351*v**5/40 - 81*v**4/8 + 25*v**3/6 - 17*v. Let w(c) be the second derivative of p(c). If w(k) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "If -1136*w + 414 + 7148*w + 342 - 2422*w**3 + 3830*w**3 - 12800*w**4 + 3072*w**3 + 14136*w**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let j(g) be the second derivative of 0 - 651/52*g**5 + 45*g**6 - 1631/26*g**4 + 378/13*g**2 - 78*g + 9/2*g**3. Suppose j(r) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let z = -41486/11961 + 1929814/59805. Find the value of n + m, where n/m is the second largest root of -2012/5*m**2 + 228*m - z + 1452*m**4 - 8492/15*m**3 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let v(p) be the second derivative of -462*p**6/5 + 68*p**5 + 3345*p**4/11 + 8480*p**3/33 + 96*p**2 + 509*p. Let v(g) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let z(t) be the second derivative of -325*t**8/84 - 390*t**7/49 - 169*t**6/56 + 351*t**5/70 + 351*t**4/56 - 229*t**3/6 + 179*t. Let h(b) be the second derivative of z(b). Let h(m) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let o(p) be the second derivative of 416*p**9/1323 + 149*p**8/147 + 71*p**7/49 + 135*p**6/112 + 9*p**5/14 + 47*p**4/12 + p - 10. Let z(g) be the third derivative of o(g). For z(s) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let p(q) be the first derivative of 6075*q**5/11 + 63450*q**4/11 + 181860*q**3/11 + 226968*q**2/11 + 131712*q/11 - 6240. Let p(k) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Let r(y) be the second derivative of 7150*y**7/147 + 1070*y**6/7 + 5049*y**5/28 + 6165*y**4/56 + 270*y**3/7 + 175*y**2/2 - 156*y. Let f(w) be the first derivative of r(w). Express the second largest root of f(s) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let t be 1/(45/160) - 180/324. If 45136*c**4 + 93186/5*c**t + 5022/5 - 2511/5*c - 95697/5*c**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let g(o) be the second derivative of 1372*o**6/11 - 3332*o**5/55 - 3591*o**4/22 + 2142*o**3/11 - 945*o**2/11 - 19*o - 7. For g(a) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let f(d) be the third derivative of -1625*d**7/14 + 4075*d**6/24 + 4235*d**5/4 + 11055*d**4/8 + 765*d**3 - 66*d**2 - 10. Express the second largest root of f(z) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "If -483*o + 175329/8*o**4 - 126 + 25361/8*o**2 + 71533/4*o**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Suppose 140*z + 160*z - 1200 = 0. If -3060/13*b + 2796/13*b**2 + 16660/13*b**3 + 432/13 - 2156*b**z = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let h(u) be the third derivative of 0 + 704/25*u**7 + 427/50*u**5 - 17*u**2 + 1533/40*u**4 + 0*u - 63/2*u**3 - 4088/75*u**6. Express the second largest root of h(o) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let n(l) be the second derivative of -1911*l**6/10 + 10199*l**5/20 + 1241*l**4/3 - 1950*l**3 + 1800*l**2 + 2*l - 667. Suppose n(m) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Let r(z) be the third derivative of 1430*z**7/9 - 12527*z**6/72 - 511*z**5/8 + 1205*z**4/16 + 45*z**3 + 21*z**2 + 18*z. For r(v) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let z = -50492/5 + 10192. Express the second largest root of -108/5 + 448*u**4 + z*u**2 - 432/5*u + 3032/5*u**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -232320/19*l**4 + 94626/19*l**2 - 1620/19 + 99924/19*l**3 + 7722/19*l, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 3218*x**2 + 13809*x**4 + 3351*x**4 + 15566*x**2 + 3295 + 665 + 26028*x - 81164*x**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let v = 700037/3 - 227479. Let 1089/2*u + v*u**4 - 6160*u**3 - 297/2 + 1089*u**2 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let m = 145 - 143. Let -179 - 122 + 16720*d**4 + 679*d - 2569*d - 23 - 108*d**m + 13602*d**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let i(n) be the third derivative of -343*n**7/24 - 34643*n**6/960 - 637*n**5/80 + 2121*n**4/64 + 63*n**3/2 + 82*n**2 - 12*n - 1. Express the second largest root of i(s) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Suppose -2*c + 140 = -148. For the polynomial -c + 458*i + 1321*i**2 + 244*i - 126*i + 6128*i**4 - 7854*i**3 + 1737*i**4, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let g(j) = 127636*j**4 - 110799*j**3 + 18855*j**2 + 2581*j - 587. Let h(m) = -63820*m**4 + 55399*m**3 - 9427*m**2 - 1291*m + 293. Let p(n) = 5*g(n) + 11*h(n). Express the second largest root of p(o) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Suppose 394*x + 66 - 456 = 1186. Suppose -50176/17*f**x - 21504/17*f**3 + 4752/17*f**2 + 3024/17*f + 324/17 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let h be ((-47350)/(-60) - 22) + (-30)/(-36). For the polynomial h*l**3 + 1440*l**4 - 108*l + 405/8 - 1125/2*l**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let q(m) be the third derivative of -121/14*m**7 + 81/20*m**3 - m**2 - 639/200*m**5 + 81/16*m**4 + 0 - 1089/80*m**6 - 18*m. For the polynomial q(n), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let c(b) be the third derivative of 115*b**7/28 - 723*b**6/112 - 9533*b**5/280 - 4209*b**4/112 - 99*b**3/7 + 81*b**2 + 2*b. Suppose c(p) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Let q = -40605 - -40607. For the polynomial 162/5 - 1773/5*s**q - 513/10*s + 537/2*s**3 + 945*s**4, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let i be 1959272/2002 - -13 - (0 + (-18)/(-66)). For i*q**2 + 10752/13*q**4 + 405/13 - 19392/13*q**3 - 3753/13*q = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Suppose 3998 - 27190*s**2 - 12750*s**4 + 5722 - 25731*s - 4968*s**2 - 25173*s**3 + 74298*s**3 - 3662*s**2 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let o(d) be the second derivative of 468*d**7/35 + 991*d**6/200 - 2237*d**5/200 - 3*d**4 + 36*d**3/5 - 23*d**2/2 + 15*d. Let u(n) be the first derivative of o(n). Express the second largest root of u(s) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let g(v) be the second derivative of -143*v**7/15 + 2011*v**6/60 - 1343*v**5/30 + 123*v**4/4 - 12*v**3 - 31*v**2/2 - 53*v. Let z(y) be the first derivative of g(y). For the polynomial z(l), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let m(w) = -6050*w**4 - 1644*w**3 + 3078*w**2 + 591*w - 327. Let i(h) = 10*h + 163. Let k be i(-16). Let f(c) = 12100*c**4 + 3286*c**3 - 6156*c**2 - 1181*c + 655. Let y(n) = k*f(n) + 7*m(n). If y(l) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Suppose 69*x + 878 = 167*x + 149*x - 110. Find the value of n + m, where n/m is the second largest root of 1296/13 + 53592/13*h**3 - 2160/13*h**2 - 6696/13*h - 66640/13*h**x = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "If -7840*d**4 - 6336 - 23268*d**3 - 1003*d**2 - 1475*d**2 + 18562*d + 2846*d - 596*d**2 + 870*d**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Suppose -77*z = 136*z + 7*z - 880. Suppose 1260/13*h**3 - 4900/13*h**z + 648/13 + 396*h**2 - 3564/13*h = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let f(p) be the first derivative of 3060*p**5 - 51185*p**4/2 + 61098*p**3 - 53334*p**2 + 18144*p - 830. Let f(a) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Let l(o) be the first derivative of -576/19*o - 18836/57*o**3 + 49 + 6910/19*o**4 - 2880/19*o**5 + 144*o**2. Express the second largest root of l(g) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For 1211*l**2 + 863*l**2 - 108 + 623*l**2 - 321*l**2 - 5950*l**4 + 94*l**3 + 243*l - 659*l**3 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Let h(d) = d**4 + d**3 - d**2 - 4*d - 2. Let u(j) = 1474*j**4 + 5122*j**3 - 3281*j**2 - 728*j + 428. Let r(o) = 10*h(o) - 5*u(o). If r(q) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let r = 893469 - 6239913/7. Find the value of n + m, where n/m is the second largest root of -1800/7 + 4480*s**3 - 26000/7*s**2 + 87040/7*s**4 - r*s = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let a(p) be the second derivative of -1287*p**6/34 + 13857*p**5/340 + 1463*p**4/68 - 1675*p**3/34 + 450*p**2/17 + 95*p. Let a(y) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let m(b) be the second derivative of -25*b**8/6 - 235*b**7/42 + 8*b**6 + 99*b**5/10 - 18*b**4 + 2*b**3/3 + b**2/2 + 23*b. Let q(u) be the second derivative of m(u). For q(n) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let w(z) be the third derivative of -640*z**7/51 + 12*z**6 + 384*z**5/85 - 189*z**4/17 + 108*z**3/17 - 2*z**2 + 499. For w(r) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let p(v) = 3640*v**4 - 243*v**3 - 3378*v**2 + 1690*v - 209. Let f(s) = -3640*s**4 + 241*s**3 + 3378*s**2 - 1689*s + 210. Let t = 260 - 266. Let b(n) = t*p(n) - 7*f(n). Let b(j) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let d(j) be the first derivative of 18000*j**5 - 2000*j**4 - 8100*j**3 + 3510*j**2 - 432*j + 651. If d(v) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Let y(o) = -7128*o**4 - 3300*o**3 + 2198*o**2 + 612*o - 222. Let a(b) = b - b**3 - 3*b**2 + 127 + 4*b**2 - 128. Let k(t) = -3*a(t) - y(t). Suppose k(i) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let v = -311 - -313. For the polynomial 1922*w**4 + 2953*w**4 - 198*w**2 - 620*w**2 - 304 + 61 - 1458*w + 4050*w**3 - 262*w**v, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let -5265/4*c**3 - 12675/2*c**4 + 16389/8*c**2 + 1701/16*c - 2187/16 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let y(j) be the third derivative of 5*j**10/108 + 95*j**9/3024 - 31*j**8/168 - 19*j**7/140 + 3*j**6/5 - 9*j**5/20 - 50*j**2. Let a(n) be the third derivative of y(n). If a(b) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let a(c) be the third derivative of 561*c**7/70 + 6163*c**6/560 - 3943*c**5/140 - 551*c**4/16 + 105*c**3/2 - 137*c**2. Let a(h) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let k(p) = 30758*p**4 + 124379*p**3 + 51241*p**2 - 45046*p + 6043. Let u(h) = 15379*h**4 + 62190*h**3 + 25621*h**2 - 22522*h + 3022. Let s(b) = 4*k(b) - 10*u(b). For s(g) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Let m(u) be the first derivative of -825*u**5/2 - 375*u**4/2 + 1485*u**3/8 + 729*u**2/16 - 81*u/2 + 479. For the polynomial m(v), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let p(m) be the second derivative of 81/5*m**2 + 8 + 21/20*m**4 - 288/5*m**6 - 3*m + 603/20*m**3 - 1608/25*m**5. For the polynomial p(k), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -3617*i**4 - 2805*i + 15890*i**4 + 77 + 823 - 9365*i**2 + 16392*i**4 + 13405*i**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "If -28000*h**4 + 16380/11*h - 8160/11*h**2 + 2160/11 - 212780/11*h**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Let g(j) be the second derivative of -108*j**2 - 22*j - 166*j**5 + 0 + 160/3*j**6 + 174*j**3 - 19*j**4. Express the second largest root of g(w) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let u(b) be the second derivative of -539*b**6/3 - 1099*b**5/10 + 522*b**4 + 108*b**3 - 432*b**2 + 1313*b - 2. Let u(w) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Suppose v + 9 = -o, 2*o - 5*v + 3 = 6. Let f(t) = 12806*t**4 + 17274*t**3 + 8712*t**2 + 1938*t + 162. Let s(k) = -12805*k**4 - 17275*k**3 - 8712*k**2 - 1939*k - 162. Let c(a) = o*s(a) - 5*f(a). Suppose c(r) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Suppose 4*v + 5*f - 51 = 0, -1522*v + 1517*v + 3*f - 1 = 0. Express the second largest root of -110241/10*c**2 - 42588/5*c**v + 3645/2 - 5103/2*c + 201123/10*c**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let k(j) = 14860*j**4 + 12000*j**3 - 2936*j**2 - 4315*j - 869. Let p(c) = -37149*c**4 - 30000*c**3 + 7341*c**2 + 10788*c + 2172. Let v be (1/2)/(3/(41 - 11)). Let r(o) = v*p(o) + 12*k(o). If r(i) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let i(p) be the first derivative of -27423/4*p**4 - 20328/5*p**5 - 243*p - 4563*p**3 - 2997/2*p**2 - 3. Suppose i(a) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let h(d) be the first derivative of -65*d**8/33 + 603*d**7/77 - 686*d**6/55 + 567*d**5/55 - 54*d**4/11 - 2*d**3/3 + 21*d**2/2 + 79. Let b(y) be the third derivative of h(y). Suppose b(j) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let m(c) = -2*c**4 - c**3 + c**2 + 4*c + 1. Let s(f) = -14108*f**4 + 44046*f**3 - 48198*f**2 + 21832*f - 3458. Let d(q) = -2*m(q) - s(q). Let d(z) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let w be (-54)/63 + (-55620)/(-63). Express the second largest root of 189/2 - w*d + 13475/6*d**4 + 2961*d**2 - 4270*d**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let t(a) = 23009*a**4 - 47700*a**3 - 46238*a**2 - 2223*a + 1998. Let p(k) = 11504*k**4 - 23850*k**3 - 23118*k**2 - 1112*k + 1000. Let z(r) = -9*p(r) + 4*t(r). Express the second largest root of z(l) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Let u(l) be the second derivative of -2376*l**6/25 - 21123*l**5/50 + 4799*l**4/20 + 506*l**3 - 855*l**2/2 - 3232*l. Suppose u(o) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let m(g) be the third derivative of 325*g**8/42 + 5*g**7/42 - 49*g**6/3 - 3*g**5/10 + 18*g**4 - 11*g**3/2 - 42*g**2. Let y(c) be the first derivative of m(c). Let y(j) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose -712*b + 333 = -601*b. If 30144/13*m**b + 1512/13*m**2 - 2700/13*m - 56320/13*m**4 + 324/13 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let b(f) = 37262*f**4 + 974*f**3 - 10044*f**2 - 84*f + 546. Let q(l) = 37263*l**4 + 973*l**3 - 10042*l**2 - 82*l + 545. Let x(h) = -5*b(h) + 6*q(h). Let x(t) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let s(p) be the second derivative of 35*p**8/6 + 21*p**7/8 - 89*p**6/8 - 27*p**5/8 + 135*p**4/8 + 7*p**3/3 + 27*p. Let b(q) be the second derivative of s(q). If b(i) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let a(h) be the third derivative of 1183*h**7/15 + 637*h**6/60 - 4813*h**5/30 - 325*h**4/12 + 100*h**3 - 180*h**2. For a(o) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let h(a) be the third derivative of -24*a**7/5 + 2231*a**6/120 - 122*a**5/5 + 99*a**4/8 + 4406*a**2. If h(q) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Let c = -282383 - -3682349/13. For the polynomial 1080/13 - 42350/13*r**4 + 52030/13*r**3 - c*r**2 - 3870/13*r, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let m(j) = 15 - 9*j. Let p be m(-21). Find the value of n + m, where n/m is the second largest root of -p - 120 + 28160*o**4 + 2232*o**2 + 17885*o**3 + 4003*o**3 - 1620*o = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let u(a) be the third derivative of -242/21*a**7 - 108/17*a**3 + 0*a + 0 + 1397/170*a**6 + 122*a**2 - 9/2*a**4 + 801/85*a**5. Let u(d) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Let l be (-150)/(4806/(-477) - -10). If -4375/3*a**4 - 5625/2*a**3 - l*a**2 - 1215/2*a - 135/2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let n(i) be the first derivative of 2112*i**5/95 + 2722*i**4/19 + 2852*i**3/57 - 9036*i**2/19 + 5760*i/19 + 8127. Let n(j) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For -6729*c**4 - 4523*c**4 - 1772*c**2 - 550*c**2 + 162 + 2144*c**4 + 837*c - 15686*c**4 - 18543*c**3 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let f be ((-126)/(-14))/((-7)/(-45)). Let -11670/7*z**3 + f - 1200*z**4 - 3483/7*z**2 + 972/7*z = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let k(n) = n**3 - 29*n**2 + 54*n + 2. Let j be k(27). For the polynomial 11125/8*u**3 - 2115/8*u - 4375/4*u**4 - 375/2*u**j + 135/2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let i(r) be the second derivative of 303212*r**6/75 + 248381*r**5/25 + 67039*r**4/15 - 9576*r**3/5 - 8064*r**2/5 - 740*r. Suppose i(z) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let m(g) be the first derivative of -11264*g**7/273 - 448*g**6/15 + 3400*g**5/39 + 5494*g**4/39 + 1120*g**3/13 + 3*g**2 - 2*g + 86. Let j(q) be the second derivative of m(q). Suppose j(a) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let f(z) = 9447*z**4 - 18906*z**3 - 23220*z**2 - 591*z + 2694. Let x(w) = -9448*w**4 + 18909*w**3 + 23222*w**2 + 589*w - 2696. Let u(h) = 2*f(h) + 3*x(h). Express the second largest root of u(t) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let k(v) = -11002*v**4 - 3077*v**3 + 6978*v**2 + 795*v - 898. Let f(x) = 11003*x**4 + 3078*x**3 - 6977*x**2 - 795*x + 897. Let m(z) = 2*f(z) + 3*k(z). Express the second largest root of m(u) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let t(u) = -91476*u**4 + 61503*u**3 + 8649*u**2 - 11025*u + 1620. Let k(y) = -22869*y**4 + 15376*y**3 + 2162*y**2 - 2756*y + 405. Let q(j) = 9*k(j) - 2*t(j). If q(z) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let x(b) = 7040*b**4 + 186*b**3 - 1569*b**2 - 27*b + 78. Let j(a) = -9413*a**2 + 25*a - 187*a + 1118*a**3 + 469 + 36678*a**4 + 26994*a**4 - 21432*a**4. Let m(h) = -6*j(h) + 34*x(h). Let m(k) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let o(t) be the first derivative of 1210*t**6 + 22*t**5 - 5645*t**4/4 - 1065*t**3 - 675*t**2/2 - 41*t + 13. Let l(m) be the first derivative of o(m). For the polynomial l(b), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 15405*j - 31850*j**4 + 9134*j**3 + 9780*j**2 - 16530*j - 540 - 699*j**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Suppose 98 = -12*f + 38. Let t(u) = -15395*u**4 + 16255*u**3 - 3132*u**2 - 1193*u + 329. Let m(w) = -7698*w**4 + 8128*w**3 - 1566*w**2 - 596*w + 164. Let v(g) = f*m(g) + 2*t(g). Express the second largest root of v(b) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Suppose 19210*j**3 - 8250*j**2 + 18066*j**4 - 448 + 756 - 63320*j**4 + 29674*j**3 - 3636*j + 556 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Suppose -4*q + 2548 = -4*o, -45574*o - 2563 = -4*q - 45571*o. If -35200/7*u**4 + 11240/21*u**3 - 144/7 - 276/7*u + q*u**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let x(j) be the second derivative of 4785*j**6/7 - 22695*j**5/14 - 3992*j**4 - 18780*j**3/7 - 5616*j**2/7 - 4*j + 453. If x(b) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -324*u**3 - 7931*u + 16452*u**2 - 4093*u + 2007 - 2272*u**4 - 4448*u**4 + 261 + 1468*u**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let m be ((-314)/18*-3)/(2/30). For the polynomial 11*l + 1150*l + m*l**2 + 5938*l**4 - 4536*l**3 + 1989*l - 5337*l**2 - 450 + 1550*l**4, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let h(g) be the third derivative of 154*g**7/5 + 25697*g**6/600 - 14273*g**5/600 - 16961*g**4/240 - 49*g**3 + 2*g**2 - 113. For the polynomial h(o), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let p(f) = -f**2 - 2*f - 7. Let r be p(0). Let u(h) = -23107*h**4 - 12563*h**3 + 6415*h**2 + 4583*h + 641. Let t(j) = 11553*j**4 + 6282*j**3 - 3207*j**2 - 2292*j - 321. Let x(i) = r*t(i) - 3*u(i). Express the second largest root of x(o) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let r(d) be the first derivative of 1815/19*d**5 + 4 - 1296/19*d**2 + 3795/38*d**4 - 432/19*d - 767/19*d**3. For r(s) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let b(f) = 11548*f**4 - 11565*f**3 + 1699*f**2 + 1049*f - 243. Let m(r) = 23096*r**4 - 23131*r**3 + 3398*r**2 + 2097*r - 487. Let z(g) = -5*b(g) + 2*m(g). Let k(h) = 80835*h**4 - 80940*h**3 + 11892*h**2 + 7356*h - 1686. Let w(n) = 2*k(n) + 15*z(n). If w(s) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let q = -451 + 455. Let h(u) = u**4 - u**2 - u - 1. Let o(m) = 4397*m**4 + 6810*m**3 + 3810*m**2 + 921*m + 84. Let w(n) = q*o(n) + 12*h(n). For the polynomial w(c), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let r(y) = -35006*y**4 - 16506*y**3 + 4050*y**2 + 3117*y + 411. Let d(x) = -105019*x**4 - 49519*x**3 + 12150*x**2 + 9353*x + 1234. Suppose 0 = -6*c - 4*c + 190. Let j(q) = c*r(q) - 6*d(q). Suppose j(h) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let x(r) be the second derivative of -14560*r**6/19 - 17838*r**5/19 + 59620*r**4/19 - 38205*r**3/19 + 8775*r**2/19 + 1569*r. Suppose x(s) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "If -3024/13 - 23760/13*d**4 + 1782/13*d + 9714/13*d**3 + 33240/13*d**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of -18851606*h + 18871154*h + 33800*h**4 - 70460*h**3 - 3024 - 21588*h**2 + 8124*h**2 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let r(m) be the third derivative of 7*m**7/4 + 2947*m**6/80 - 72007*m**5/200 - 2923*m**4/16 + 3135*m**3/2 + 3*m**2 + 32*m + 1. For r(i) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Suppose 0 = 1187*d - 212194 - 15710. Suppose -1020*c - 1448*c**2 - d + 8800/9*c**4 + 1060/9*c**3 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let n(i) be the third derivative of -104*i**7/7 + 1043*i**6/20 - 1644*i**5/25 + 3339*i**4/80 - 297*i**3/20 + 2*i**2 + 173*i + 2. Suppose n(x) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let w(u) = 10781*u**3 - 2*u**2 + 1. Let r be w(1). For the polynomial -2735*f + r*f**4 + 19116*f**2 + 546 - 3205*f + 102 - 25116*f**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let u = 29719 + -20479. Express the second largest root of 6092*x**2 - 192 - 164 - 2661*x**3 - 1415*x**3 - 604 + 1408*x - u*x**4 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let s(y) be the first derivative of -728*y**5/3 - 16283*y**4/9 - 15076*y**3/9 - 26*y**2 + 372*y - 3029. Express the second largest root of s(o) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let m = 87 + -85. For the polynomial -32032*x**4 + 879*x**2 + 864 + 50*x**m - 24716*x**3 + 259*x**2 + 4536*x, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let w(l) = -4319*l**4 - 4029*l**3 + 8770*l**2 - 1432*l - 856. Let o(v) = -1439*v**4 - 1343*v**3 + 2923*v**2 - 477*v - 285. Let y(i) = -8*o(i) + 3*w(i). For y(q) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -36960/13*y**4 - 29476/13*y**3 + 432/13 + 2196/13*y - 3072/13*y**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let -9849 + 108275*z**2 - 171600*z**4 - 35730*z + 849 + 330800*z**2 - 681770*z**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let k(p) = -20800*p**4 - 56171*p**3 - 54984*p**2 - 23057*p - 3490. Let a(h) = -2600*h**4 - 7021*h**3 - 6873*h**2 - 2882*h - 436. Let o(d) = 17*a(d) - 2*k(d). Suppose o(v) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let k(w) = -5*w**2 + 19*w + 7. Let u be k(4). For the polynomial -1728*t + 2973*t**2 - 8316*t**4 + 4158*t - 675 + 1832*t**3 - 9860*t**u, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let 27373*c**4 - 12349*c**4 + 584*c**2 + 62752*c**3 - 6624*c - 56 + 22596*c**4 + 18484*c**2 - 2104 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let f(j) be the third derivative of -143*j**10/945 + 229*j**9/15120 + 253*j**8/1120 - 3*j**7/280 - 3*j**6/10 + j**5/12 - j**4/24 + 94*j**2 - j. Let z(v) be the third derivative of f(v). Suppose z(p) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let j(r) = -r**4 - 2*r**3 - r**2 - 16*r - 3. Let k(t) = 173639*t**4 - 1975928*t**3 + 5413042*t**2 + 1228448*t - 193606. Let a(z) = 2*j(z) - k(z). Suppose a(d) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Let s(f) be the third derivative of -144*f**7/17 + 6791*f**6/170 - 227*f**5/5 - 735*f**4/34 + 1350*f**3/17 - 4*f**2 - 27. For the polynomial s(j), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Let t(i) be the second derivative of 243/22*i**2 - 49/2*i**6 + 270/11*i**3 + 4 + 10*i + 351/22*i**4 - 1071/55*i**5. If t(u) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let c(b) = -41993*b**4 - 60136*b**3 + 31814*b**2 + 76268*b + 26723. Let n(j) = 13998*j**4 + 20046*j**3 - 10609*j**2 - 25423*j - 8908. Let h(s) = -2*c(s) - 7*n(s). Find the value of n + m, where n/m is the second largest root of h(r) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "For -1863/4*u + 9075*u**4 + 20955/4*u**3 - 405/8 - 2187/8*u**2 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let s(b) be the second derivative of 18513*b**6/23 - 45705*b**5/46 - 68745*b**4/46 - 1305*b**3/23 + 8100*b**2/23 - 8*b - 105. Suppose s(u) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Suppose 15*d = 1041 + 13914. Suppose -d*v**2 - 38236*v**3 - 131*v**2 + 164 + 2844*v + 268 - 62920*v**4 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let v(l) be the first derivative of -2240*l**6/3 - 16032*l**5/11 - 12888*l**4/11 - 5472*l**3/11 - 1296*l**2/11 - 38*l + 2. Let o(k) be the first derivative of v(k). If o(q) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let g = -514 - -867. Let -g + 1204*a + 281*a + 1253 - 11869*a**2 + 13801*a**4 + 789*a**2 - 10560*a**3 + 19479*a**4 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let o(y) be the first derivative of 1182*y**3 - 20 - 3375/2*y**4 + 324*y - 2470*y**5 + 1215*y**2. If o(m) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let d(a) = -2008 + 1457*a - 54898*a**4 - 6433*a**3 + 12881*a**4 + 720*a + 20981*a**2. Let i(r) = 14006*r**4 + 2144*r**3 - 6993*r**2 - 726*r + 669. Let n(w) = -6*d(w) - 17*i(w). Suppose n(j) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let v(z) be the third derivative of 704*z**7/5 - 9677*z**6/15 + 5683*z**5/5 - 5765*z**4/6 + 400*z**3 - 2079*z**2. Suppose v(x) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let s(d) be the third derivative of -169*d**9/2160 - 13*d**8/35 + 159*d**7/140 - 6*d**6/5 + 27*d**5/40 - d**4/12 + 11*d**3/6 + 30*d**2. Let j(c) be the second derivative of s(c). Let j(r) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let m(b) = b**3 - b**2 - 9*b + 1. Let a(s) = -7007*s**4 + 3526*s**3 + 848*s**2 - 630*s + 79. Let r(v) = 5*a(v) + 10*m(v). Find the value of n + m, where n/m is the second largest root of r(h) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let r(u) = -28800*u**4 - 2141511*u**3 - 486321*u**2 + 873063*u - 160110. Let m(g) = 14400*g**4 + 1070756*g**3 + 243160*g**2 - 436534*g + 80055. Let i(p) = -9*m(p) - 4*r(p). Suppose i(k) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Let d(z) be the third derivative of -1539*z**7/182 - 4293*z**6/130 - 14293*z**5/260 - 657*z**4/13 - 360*z**3/13 - 2*z**2 - 122*z. For d(l) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Suppose -4*t + 4*r = 24, r + 2 = 3*t - 4*t. Let u(x) = 35530*x**4 + 44114*x**3 + 20470*x**2 + 4207*x + 324. Let p(a) = -35530*a**4 - 44113*a**3 - 20471*a**2 - 4208*a - 324. Let y(q) = t*u(q) - 5*p(q). Find the value of n + m, where n/m is the second largest root of y(m) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let m(w) be the second derivative of 3080/27*w**6 + 1879/18*w**5 + 0 - 30*w**2 - 385/6*w**3 - 895/36*w**4 - 30*w. If m(h) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let n(l) = 739187*l**4 - 911397*l**3 + 373886*l**2 - 59683*l + 3240. Let c(h) = 123198*h**4 - 151898*h**3 + 62314*h**2 - 9947*h + 540. Let m(t) = -13*c(t) + 2*n(t). Let m(g) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let o(w) be the second derivative of -108*w**6/5 + 39231*w**5/35 + 153507*w**4/14 + 342431*w**3/14 - 621639*w**2/14 - 4431*w. Let o(f) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Suppose -2*u - 264 = -2*t, -134*u + 132*u = 3*t - 366. For the polynomial t*f**3 - 81/10*f - 243/10 - 2640*f**4 + 2592/5*f**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let l(q) be the third derivative of 352*q**7/3 - 4583*q**6/15 - 2999*q**5/5 + 303*q**4 + 630*q**3 + 320*q**2. Express the second largest root of l(w) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let c = -4/30843 + 13601771/61686. Find the value of n + m, where n/m is the second largest root of c*f - 15400/3*f**4 - 126 + 3213/2*f**2 - 4795/3*f**3 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let b(z) be the first derivative of -224*z**6/3 - 230*z**5 - 1115*z**4/4 - 2775*z**3/16 - 945*z**2/16 + 57*z - 6. Let k(w) be the first derivative of b(w). Find the value of n + m, where n/m is the second largest root of k(i) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let v(z) = 12090*z**4 + 46310*z**3 + 53623*z**2 + 10785*z - 9408. Let w(g) = 6044*g**4 + 23155*g**3 + 26812*g**2 + 5393*g - 4704. Let s(x) = -3*v(x) + 5*w(x). Let s(a) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Let t(l) be the first derivative of 5016*l**5 - 243331*l**4/28 + 41723*l**3/7 - 14157*l**2/7 + 2376*l/7 + 3399. Find the value of n + m, where n/m is the second largest root of t(m) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let h(c) = 595*c + 9522. Let t be h(-16). Let -96*z**3 + 576/11 - 7532/11*z**t + 480/11*z + 1540*z**4 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let c(a) be the first derivative of 1573*a**8/432 + 6259*a**7/1512 - 221*a**6/216 - 91*a**5/24 - 5*a**4/2 - 28*a**3/3 - 34. Let o(f) be the third derivative of c(f). For o(l) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let k(b) be the first derivative of 840*b**5/11 - 29655*b**4/44 + 5392*b**3/11 + 15363*b**2/22 - 9180*b/11 + 1584. For k(f) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let p(v) be the first derivative of 352*v**6 + 13542*v**5/65 - 2940*v**4/13 - 1116*v**3/13 + 1296*v**2/13 - 42*v + 3. Let j(z) be the first derivative of p(z). Express the second largest root of j(c) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let a(o) be the third derivative of -105*o**7/19 + 5803*o**6/152 - 3886*o**5/95 - 1953*o**4/152 + 828*o**3/19 - 9138*o**2. For the polynomial a(d), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Let w(y) be the first derivative of -288288*y**5/17 - 305244*y**4/17 + 132282*y**3/17 + 18387*y**2/17 - 6804*y/17 + 6913. Find the value of n + m, where n/m is the second largest root of w(j) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Let d(y) = -18154*y**4 - 16333*y**3 - 1919*y**2 + 1215*y + 245. Let m(i) = -54464*i**4 - 48998*i**3 - 5758*i**2 + 3645*i + 736. Let n be ((-12)/3)/(-12)*21. Let h(p) = n*d(p) - 2*m(p). Express the second largest root of h(q) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let l(p) = -p**4 + p**3 + p - 1. Let b(q) = -1926*q**4 - 299*q**3 + 918*q**2 + 109*q - 82. Suppose -6*w = -42 + 36. Let m(j) = w*b(j) - l(j). For the polynomial m(y), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let d(l) be the third derivative of -70*l**7/57 - 1715*l**6/114 - 5291*l**5/285 + 17743*l**4/114 - 3944*l**3/19 - 1894*l**2. Find the value of n + m, where n/m is the second largest root of d(m) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let j(h) be the first derivative of -15093/14*h**2 - 193479/28*h**4 - 23 - 3861*h**3 - 34606/7*h**5 - 1053/7*h. For j(w) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let g(z) be the third derivative of 35*z**7/6 + 56*z**6/3 + 17*z**5/2 - 120*z**4/7 - 45*z**3/2 + 35*z**2 - 5. If g(x) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let z(t) be the second derivative of -1664*t**7/21 + 1096*t**6/5 - 1251*t**5/5 + 153*t**4 - 54*t**3 - 35*t**2/2 + 4*t - 14. Let r(d) be the first derivative of z(d). If r(v) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let h(g) = -21598*g**4 + 31622*g**3 - 9818*g**2 - 2623*g + 1123. Let t(p) = 64793*p**4 - 94867*p**3 + 29453*p**2 + 7868*p - 3368. Let z(w) = -7*h(w) - 2*t(w). For the polynomial z(i), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let s(y) be the third derivative of -275*y**7/21 + 455*y**6/24 + 165*y**5/4 - 81*y**4/8 - 63*y**3/2 + 209*y**2 + y. If s(c) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let m(o) = -9300*o**4 + 284293*o**3 + 29749*o**2 - 68590*o + 10773. Let q(l) = l**4 + 19*l**3 + l**2 + 2*l. Let c(b) = 4*m(b) + 20*q(b). If c(t) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let t(b) be the second derivative of 5236*b**6/19 - 26937*b**5/95 - 805*b**4/19 + 2256*b**3/19 - 864*b**2/19 - 2*b + 595. For the polynomial t(f), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Let j(b) be the first derivative of -1950*b**5/11 - 4725*b**4/11 + 4630*b**3/11 + 1008*b**2 - 12960*b/11 - 202. Let j(z) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Suppose 11235*m**4 + 2149*m**3 + 11888*m**3 + 324 - 734*m**2 + 3965*m**2 - 2565*m - 28287*m**4 - 9975*m**4 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 1458/7*o - 4620*o**4 - 9693/7*o**2 + 81 - 5316*o**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let x be (3/4*78)/(-69*(-665)/1691190). Find the value of n + m, where n/m is the second largest root of x*n - 30888*n**4 - 38376/7*n**2 + 4212/7 - 210873/7*n**3 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let v(p) be the first derivative of 1225*p**6/24 - 2205*p**5/32 - 15*p**4/32 + 675*p**3/16 - 405*p**2/16 - 12*p - 19. Let q(z) be the first derivative of v(z). For the polynomial q(l), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Suppose 3*v = -3*l + 12, 6*v - 2*l - 7 = 3*v. Let 3281*q**3 + 20453*q**4 - 4920*q**2 + 487*q**v - 6310*q**4 + 5357*q**4 + 1382*q**3 - 234*q + 216 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let i(m) be the first derivative of -2156*m**5 + 3521*m**4 - 2288*m**3/3 - 1312*m**2 + 768*m + 344. Find the value of n + m, where n/m is the second largest root of i(t) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -10698*s**3 - 16296/5*s - 1872/5 - 3465*s**4 - 47817/5*s**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let v(i) be the first derivative of 777*i**5/2 - 10953*i**4/16 + 8721*i**3/20 - 4779*i**2/40 + 243*i/20 - 2302. For the polynomial v(p), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let h(y) be the first derivative of -484*y**6/3 + 5797*y**5/10 - 26939*y**4/32 + 10131*y**3/16 - 2079*y**2/8 + 241*y - 151. Let t(f) be the first derivative of h(f). Let t(m) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let c(l) be the second derivative of 455*l**6/6 - 6401*l**5/44 - 57835*l**4/132 + 4175*l**3/22 + 315*l**2 - 246*l + 1. Express the second largest root of c(n) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let l = -20264 + 20266. Express the second largest root of 405/2*t**l + 405/2*t - 600*t**3 + 162/5 - 750*t**4 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let b be 129 + 8 - (154/(-22) - -18). If 26600/3*y**3 - 123200/9*y**4 - 168*y**2 + b - 798*y = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose 1836/5 - 4131*d + 21420*d**4 + 86139/5*d**2 - 31552*d**3 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let d(c) = -51757*c**4 + 8468*c**3 + 42173*c**2 + 16475*c + 1702. Let m(s) = 8626*s**4 - 1411*s**3 - 7029*s**2 - 2746*s - 284. Let j(q) = 6*d(q) + 39*m(q). If j(n) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let o(g) be the third derivative of -220*g**7/7 - 1959*g**6/8 + 9457*g**5/20 + 4509*g**4/4 - 1476*g**3 - 2*g**2 + 725*g. For the polynomial o(j), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let c be (-108)/15*((-243425)/770 + -35). If c*q**2 - 7830/11*q + 810/11 + 24500/11*q**4 - 43050/11*q**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let q(y) be the third derivative of -416*y**7/161 + 4788*y**6/115 + 1905*y**5/92 - 19267*y**4/184 + 1974*y**3/23 + 2671*y**2. Suppose q(z) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let v be (-153972)/(-702) - (-5 - -41). Suppose 1795/2*z - 15695/6*z**3 - 210 + 1925*z**4 - v*z**2 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let g(b) = -32340*b**4 + 13664*b**3 + 955*b**2 - 1017*b + 96. Let f(p) = 3 - p**2. Let k(z) = 4*f(z) + g(z). Suppose k(l) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let p(q) be the first derivative of -6080*q**5 + 9865*q**4 - 5854*q**3 + 1629*q**2 - 216*q - 498. Let p(l) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let i(s) be the first derivative of 81081*s**5/5 + 143397*s**4/20 - 57591*s**3/5 - 4617*s**2/10 + 8748*s/5 + 996. For the polynomial i(k), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let p(l) be the second derivative of -6 + l - 3051/28*l**5 + 1053/14*l**3 + 715/7*l**6 - 207/7*l**4 - 243/7*l**2. Express the second largest root of p(m) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "If -2970/13 + 42174/13*p**2 + 12672*p**4 + 177056/13*p**3 - 8316/13*p = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let i = -4537 + 4539. If -324/7 + 5580/7*x**i + 7200/7*x**3 - 648/7*x - 22000/7*x**4 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose 864*y + 1668*y**2 - 28600/9*y**4 - 192 - 63860/9*y**3 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let w be (-10 + 8)*2/(-2). For 1003*n**3 + 5717*n**3 - 379*n + 162 - 6400*n**4 - 600*n**2 - 588*n**w - 215*n = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let y(f) be the first derivative of -2310*f**5/13 + 147165*f**4/52 + 1059*f**3/13 - 89613*f**2/26 - 21627*f/13 + 2410. For the polynomial y(w), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let q(r) be the third derivative of 0*r + 585/4*r**5 + 45/2*r**4 + 20*r**2 - 209/4*r**6 + 0 - 4840/21*r**7 - 135/2*r**3. For the polynomial q(v), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let i(u) be the third derivative of 11*u**10/70 + 2983*u**9/10080 - 61*u**8/2240 - 69*u**7/140 - 9*u**6/16 - 3*u**5/10 - u**4/12 + u**2 - 34. Let z(s) be the third derivative of i(s). For the polynomial z(a), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let n(f) be the second derivative of 99*f**6 + 411*f**5/4 - 1407*f**4/20 - 1233*f**3/10 - 81*f**2/2 + 95*f - 13. If n(t) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let p(t) be the second derivative of 125*t**9/396 - 1825*t**8/3696 + 85*t**7/1848 + 73*t**6/176 - 9*t**5/22 - 25*t**4/6 + 44*t. Let d(k) be the third derivative of p(k). Let d(w) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let q(h) = -11557*h**4 - 12060*h**3 - 664*h**2 + 2260*h + 478. Let v(m) = -5778*m**4 - 6030*m**3 - 332*m**2 + 1130*m + 239. Let i(p) = 3*q(p) - 7*v(p). Let g(w) = -23100*w**4 - 24120*w**3 - 1326*w**2 + 4521*w + 957. Let k(z) = -4*g(z) - 15*i(z). Express the second largest root of k(o) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let g(a) be the third derivative of -44*a**10/4095 - 1679*a**9/49140 + 311*a**8/3276 + 1081*a**7/16380 - 11*a**6/39 + 2*a**5/3 - 3*a**2 + 2*a. Let c(m) be the third derivative of g(m). Let c(q) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let -7344*u**2 - 2947*u**4 - 6247*u**3 - 1472*u**4 - 7819*u**3 - 2731*u**4 - 1836*u - 162 + 1886*u**3 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let t be ((4 + -2 - -1) + 1 - 0) + 69/(-69). For the polynomial -3096/13*j + 432/13 - 3584/13*j**4 - 2944/13*j**t + 6792/13*j**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -2800*r**4 + 10670*r**3 + 1644 + 2448 - 1092 - 4544*r**2 - 5510*r, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let z(v) be the first derivative of -855*v**5 + 1092215*v**4/32 - 1857307*v**3/4 + 34276095*v**2/16 + 1809864*v + 253. For z(p) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Suppose -4800/13 + 115080/13*s**3 - 19960/13*s - 330750/13*s**4 + 89630/13*s**2 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Suppose 0 = -5*q - 4*w + 8, 8 = -3*w - 1. If 78*t**2 + 1201*t**3 - 63 - 3505*t**3 + 2240*t**q + 324*t - 18 + 183*t**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let 420 - 10825/7*t**3 - 11710/7*t**2 + 1675*t + 250*t**4 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let k(z) = -28*z - 15. Let x be k(-4). Express the second largest root of 648*u**2 - 621*u + x + 3038*u**3 - 8800*u**4 - 16 + 1342*u**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let -3003*f**4 + 8136/7*f + 1728/7 + 1434/7*f**2 - 3525*f**3 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let q(k) be the second derivative of 6655*k**6/6 - 3993*k**5/4 - 2475*k**4/4 + 1935*k**3/2 - 405*k**2 - 29*k - 7. Let q(d) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let x(o) be the first derivative of 2240/11*o**3 + 126/11*o**2 - 1108/11*o**4 - 2688/11*o**5 + 54 - 540/11*o. For the polynomial x(l), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of -52052/15*i**4 - 144/5 - 4108/15*i**3 + 36/5*i + 3468/5*i**2 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let o(g) be the first derivative of -2 + 320*g**3 - 540*g + 10010*g**5 - 3285/2*g**2 + 34715/4*g**4. Let o(w) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let p(f) = 24197*f**4 - 20460*f**3 + 1398*f**2 + 1833*f - 324. Suppose -5*v - 2*m - 21 = 0, -52*v + 4*m + 21 = -55*v. Let z(n) = 24196*n**4 - 20460*n**3 + 1396*n**2 + 1832*n - 324. Let k(h) = v*z(h) + 4*p(h). Find the value of n + m, where n/m is the second largest root of k(r) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let j(h) be the second derivative of h**9/36 + 45*h**8/896 - 93*h**7/2800 - 27*h**6/160 - 81*h**5/400 - 3*h**4/4 - 31*h. Let q(n) be the third derivative of j(n). For the polynomial q(a), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let t(i) be the first derivative of -23814*i**5/5 - 2457*i**4/4 + 2878*i**3 + 1017*i**2/2 - 540*i + 1487. If t(z) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let u be ((-72275)/(-105))/59*(-64)/(-10). Express the second largest root of -u*n - 2912/9*n**2 + 0 + 238/3*n**3 + 10010/9*n**4 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Let f(t) = -20167*t**4 + 8504*t**3 + 9015*t**2 - 2091*t - 1200. Let v(j) = 6722*j**4 - 2835*j**3 - 3005*j**2 + 697*j + 400. Let x(z) = -3*f(z) - 8*v(z). Let u(r) = -6724*r**4 + 2832*r**3 + 3007*r**2 - 698*r - 401. Let h(d) = -5*u(d) - 4*x(d). If h(w) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let q(w) be the first derivative of -194 + 1375*w**5 - 4250*w**4 + 15125/3*w**3 - 2820*w**2 + 720*w. For the polynomial q(c), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 4504*g + 3704*g - 399 + 109263*g**4 - 28401*g**2 - 33 - 9207*g**3 - 5511*g**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let u be ((-19)/(-2))/((-195)/66 + 3). Suppose 297*y + 324 + 3846*y**4 - 735*y**3 + 3713*y**4 - 3492*y**2 - u*y**4 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let m(a) = -a**3 + 3*a**2 + a + 3. Let g be m(0). Express the second largest root of 23114*z - 10824*z**2 + 13320*z**g - 714*z + 31570*z**2 + 3840 - 14175*z**4 + 18934*z**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Suppose 44*l - 1835 = -304*l - 83*l - 542. For -11520/7*p**l - 1305/7*p**2 + 405/7 + 1620/7*p - 1600*p**4 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let c(b) be the third derivative of -11*b**10/720 + 269*b**9/20160 + 107*b**8/2352 - 13*b**7/560 - 3*b**6/28 - b**5/30 - b**4/3 - 12*b**2 + 5*b. Let z(w) be the third derivative of c(w). Express the second largest root of z(n) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let g(i) be the second derivative of -252*i**6/13 - 1017*i**5/65 + 1375*i**4/26 + 2279*i**3/26 + 630*i**2/13 - 883*i + 2. For the polynomial g(t), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 237*a**3 - 1848*a**4 + 8361/11*a**2 - 648/11 - 702/11*a, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Suppose -153*k + 16 = -149*k. Express the second largest root of 22197*y**3 + 6174*y**k - 57 + 9657*y + 261 + 238 + 23268*y**2 + 962 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Let u(w) = 172384*w**4 + 57841*w**3 - 15727*w**2 - 7390*w - 644. Let m(a) = -a**4 - a**3 + a**2 - 2*a - 1. Let x(n) = -4*m(n) - u(n). Suppose x(t) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let l(w) be the first derivative of 18326*w**5/5 + 3577*w**4 - 338*w**3 - 1314*w**2 - 432*w + 432. For the polynomial l(s), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let -533*y**2 + 845*y**2 + 5238*y**2 + 126*y - 12160*y**4 + 190*y**3 - 1086*y**3 - 540 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Suppose 342*z - 312 - 636 = 26*z. If -2025/13*w + 11835/13*w**z - 2200*w**4 - 810/13 + 8820/13*w**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let v(c) be the third derivative of 3*c**8/2 + 1189*c**7/1155 - 1649*c**6/495 - 123*c**5/55 + 60*c**4/11 + 55*c**3/3 - c**2 - 35*c. Let a(d) be the first derivative of v(d). Let a(l) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let n(d) = -2*d**4 + d + 2. Let s(c) = 67381*c**4 + 13300*c**3 - 24210*c**2 - 5943*c + 669. Let o(t) = 3*n(t) + s(t). For o(g) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Let o(r) be the third derivative of -95*r**10/756 - 115*r**9/2352 + 131*r**8/392 + 9*r**7/196 - 9*r**6/14 - r**5/12 - 54*r**2. Let y(x) be the third derivative of o(x). Let y(w) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Let o(z) be the second derivative of -608*z**6 - 3254*z**5/3 - 31465*z**4/54 + 200*z**3/9 + 125*z**2 - 1112*z. If o(y) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let v(x) be the second derivative of 85*x**9/216 - 141*x**8/4928 - 25*x**7/56 - 9*x**6/176 + 27*x**5/88 - 119*x**4/6 + 8*x + 13. Let j(f) be the third derivative of v(f). Let j(i) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Let f be (104/28 - 4)*(-207 + 4). Suppose -13552*p**3 + 60 - f*p - 2748*p**2 + 328 - 11858*p**4 - 118 + 1066*p = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Suppose 12860/17*k**3 - 299900/17*k**2 + 28600*k**4 + 30000/17 + 22000/17*k = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let x(n) be the third derivative of -17*n**9/16 - 2309*n**8/2240 + 257*n**7/84 + 9*n**6/5 - 36*n**5/5 - 9*n**4/8 - n**3/2 - 121*n**2. Let r(v) be the second derivative of x(v). Suppose r(i) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 3600*l + 11252*l**3 + 5500*l**4 + 232 + 11334*l**2 + 380*l**4 + 146 + 2916*l**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let -19944/7*f**2 - 364*f**4 - 1904*f**3 - 1296*f - 1188/7 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let u(o) be the second derivative of -819*o**6/2 - 35913*o**5/10 - 2019*o**4 + 2547*o**3 + 3969*o**2/2 - 4*o + 35. Express the second largest root of u(t) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of 185479/10*u**3 - 12236/5*u + 672 - 84084/5*u**4 - 14217/5*u**2 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Let -176715/4*i**4 + 421869/8*i**3 + 33831/8*i - 91161/4*i**2 - 567/2 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose 7257/10*x**2 + 414/5*x - 432/5 + 735*x**4 - 2961/2*x**3 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let g = 2233794377/658105 - -289/94015. Suppose 810/7 - 540/7*a + 173030/7*a**4 + 7260/7*a**3 - g*a**2 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let i(l) be the first derivative of -1485/13*l**5 - 17 + 5325/52*l**4 + 591/13*l**3 + 324/13*l - 1917/26*l**2. For the polynomial i(u), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let c(o) be the first derivative of 2550*o**5 - 7150*o**4 + 6650*o**3 - 2574*o**2 + 432*o - 4014. If c(n) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let f(w) be the second derivative of -35*w**9/486 - 49*w**8/216 - 188*w**7/2835 + 56*w**6/81 + 64*w**5/45 + 41*w**4/12 - 37*w - 1. Let r(x) be the third derivative of f(x). For the polynomial r(b), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Let k = 26798 + -14141. Find the value of n + m, where n/m is the second largest root of -2179*c**3 - k*c**4 - 324 - 432*c - 55103*c**4 + 7987*c**3 + 9396*c**2 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let k(t) be the third derivative of 3875/54*t**4 - 56/9*t**7 + 2335/108*t**5 + 4375/54*t**3 - 1043/108*t**6 - 5*t**2 + t + 0. Suppose k(r) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Let x be ((-532)/105)/(-19) - 8096/(-15). Let 17085*u**3 + x - 21560*u**4 - 126*u - 2349*u - 1230*u**2 + 1640*u**3 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let j(w) be the first derivative of -w**5/5 - w**4/2 - w**3/3 - 61. Let k(b) = -2273*b**4 + 6964*b**3 - 6280*b**2 + 2160*b - 243. Let g(a) = 6*j(a) + 3*k(a). Express the second largest root of g(c) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let h be (-1707258)/(-70) + (-162 - -127). For the polynomial -9828/5*a + 20538/5*a**2 - 378 + 103488/5*a**4 + h*a**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 10164*u**4 - 16729 + 220981*u**2 - 18086 + 9767*u**2 + 11271 + 8514*u + 197318*u**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let u(b) be the second derivative of 275*b**9/567 + 715*b**8/756 - 242*b**7/189 - 143*b**6/180 + 77*b**5/40 - b**4/6 - 5*b**3/2 - 49*b - 2. Let v(d) be the third derivative of u(d). Express the second largest root of v(z) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let g be 24/40 - (35 + (-7264)/160 - 14/(-2)). Find the value of n + m, where n/m is the second largest root of 24057/5*w**2 - 130438/5*w**g - 891/5 - 297/5*w + 2541*w**3 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let t(q) = -q**4 + q**3 + q. Let n(y) = 3476*y**4 + 124*y**3 - 2700*y**2 + 132*y + 432. Let w be (18/21)/((-4)/(-112)). Let m(g) = w*t(g) - n(g). Suppose m(b) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let s be (-60 + 130 + -59)*28/77. Suppose -540/17 - 20280/17*t**2 - 5472/17*t - 32704/17*t**3 - 19404/17*t**s = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let p be (11/(-242))/(5/(-30)) + (-451)/(-121). Suppose -243/19 + 42900/19*r**p + 1944/19*r - 1161/19*r**2 - 21600/19*r**3 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let o(a) be the second derivative of 108*a**2 + 165*a**3 - 3*a + 4 - 539/2*a**5 - 23*a**4 - 490/3*a**6. Suppose o(p) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 121*k + 371 + 682 - 40746*k**3 + 1760*k - 7924*k**4 + 1845*k - 10233*k**2 - 10556*k**4, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "If -2448225/8*x**3 - 29835 - 907959/2*x**2 - 114075/4*x**4 - 1744821/8*x = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let s = 29340851831/12132197 - -4/1733171. Express the second largest root of 37323/7*l**2 - 121*l**3 - s*l + 297 - 39930/7*l**4 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let t(k) be the third derivative of 64*k**7/3 + 1040*k**6/33 + 25*k**5/22 - 975*k**4/44 - 180*k**3/11 - 234*k**2 - 7*k - 1. For t(b) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let -139000/13*y**2 + 207616/13*y**3 - 5280*y**4 + 9576/13 - 19632/13*y = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let f(s) = 38896*s**4 + 101904*s**3 + 40646*s**2 - 1314*s - 1632. Let d(r) = -r**3 + r. Let k(q) = -4*d(q) - 2*f(q). For the polynomial k(g), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let h(d) = 6*d**3 + d + 3. Let z(x) = -10560*x**4 - 37896*x**3 - 5721*x**2 + 21848*x - 5196. Let y(l) = -4*h(l) - z(l). Express the second largest root of y(r) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let s(n) be the third derivative of 27/5*n**5 - 1/6*n**6 + 3/10*n**4 + 0*n + 17 - 220/63*n**7 - 18/5*n**3 - n**2. Suppose s(v) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let c be 4/1*20/40. If 30*p - 354*p + 8928*p**c + 884*p**3 + 4743 - 37856*p**4 - 5175 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let u = -641445 + 10908993/17. If 972/17 + u*s - 16000/17*s**4 - 32400/17*s**3 - 4320/17*s**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let g(j) be the third derivative of 509/120*j**6 + 0 - 95*j**2 + 1/3*j**7 + 721/60*j**5 + 24*j**3 - 31*j**4 + 0*j. For the polynomial g(t), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose -12148 - 12380 + 24116 = -103*q. Let -486/7 + 7479/7*r**2 - 3300*r**q - 1215/7*r + 13500/7*r**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let l(z) be the third derivative of -24*z**2 + 0 - 429/2*z**5 + 205*z**6 - 275/6*z**7 + 405/2*z**3 - 45*z**4 + 0*z. Suppose l(a) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let p(g) be the first derivative of -77 - 1593/2*g**2 - 195*g**3 + 825*g**5 - 324*g + 4425/4*g**4. For the polynomial p(o), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let f(r) be the third derivative of 385*r**8/192 + 1457*r**7/192 + 34153*r**6/2880 + 203*r**5/20 + 21*r**4/4 - r**3/3 - 35*r**2. Let c(o) be the first derivative of f(o). Express the second largest root of c(h) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let j(o) be the second derivative of -69/2*o**3 + 2*o + 8 - 100/3*o**6 - 95/2*o**4 + 54*o**2 + 325/4*o**5. Suppose j(f) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let z be (2 + 2)/(-28)*-161. For the polynomial -27*j - 97 - 88 + z - 3640*j**4 + 1620*j**2 + 309*j**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let t(l) be the third derivative of 561*l**7/112 + 1849*l**6/640 - 2949*l**5/320 - 333*l**4/128 + 135*l**3/32 - 412*l**2. Find the value of n + m, where n/m is the second largest root of t(k) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Suppose 4*q - 5*k - 23 = 0, 0 = 3*q + k - 5*k - 18. Let g(f) = f**4 + 2*f**3 + 2*f**2 - 2*f + 1. Let h(z) = 13998*z**4 - 8804*z**3 - 4264*z**2 + 1336*z + 430. Let m(v) = q*g(v) + h(v). Suppose m(d) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Suppose 4*h - 24 = 3*k, 2*k = 3*h - 10 - 7. Suppose -336*b**2 + 59565*b**4 - 18381*b**4 - 835*b - 768 - 9993*b**h - 3453*b + 40501*b**3 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let y(t) be the first derivative of 1144*t**6/3 + 1659*t**5/10 - 3235*t**4/12 - 79*t**3/2 + 90*t**2 - 90*t + 170. Let q(k) be the first derivative of y(k). Express the second largest root of q(z) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let i(l) be the second derivative of 0 + 4236/25*l**5 - 81*l**2 + 1232/25*l**6 - 1593/20*l**3 + 3159/40*l**4 - 223*l. Let i(n) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let b(n) be the third derivative of 72/7*n**3 + 143/20*n**5 + 0 + 0*n - 1440/49*n**7 - 135/7*n**4 + 192/7*n**6 + 145*n**2. If b(l) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Suppose 13*x + 56*x = -838 + 3322. Suppose 868/5*b**2 + 9304/15*b**3 - 704*b**4 + x - 1056/5*b = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Suppose 8594*l**4 + 1442 - 58994*l**4 + 857 + 16228*l**2 - 3019 - 30050*l**3 + 3012*l + 8890*l**3 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Let a be (11/(132/(-912)))/((-63)/243). If a*t - 405/7 - 5700/7*t**3 + 825*t**4 - 954/7*t**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let h = -43628 - -43632. Suppose -25410/19*o**h - 1944/19*o + 486/19 + 26136/19*o**3 - 4644/19*o**2 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let j(y) be the third derivative of -75*y**7/2 + 3925*y**6/12 - 9403*y**5/12 - 345*y**4 + 1560*y**3 - 11*y**2 - 34*y. Suppose j(l) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Suppose 729/17 - 6966/17*a - 23100/17*a**4 + 20061/17*a**2 - 9540/17*a**3 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let k(l) be the first derivative of -55*l**8/6 - 1765*l**7/42 + 259*l**6/90 + 1264*l**5/15 + 88*l**4 + 2*l**3/3 + 5*l**2/2 - 35. Let c(g) be the third derivative of k(g). Find the value of n + m, where n/m is the second largest root of c(u) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let s be (-6)/2 - (72 + -77). Suppose 1134 - 8342*o**2 + 37935*o**3 + 9155*o**4 + 3495*o**4 + 26541*o**2 + 10449*o + 14273*o**s = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let r(t) = -39244*t**4 + 2210740*t**3 + 3154934*t**2 + 1452802*t + 218440. Let b(a) = 5606*a**4 - 315820*a**3 - 450705*a**2 - 207543*a - 31206. Let l(q) = 22*b(q) + 3*r(q). Suppose l(x) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let w(o) be the third derivative of -13*o**7/2 + 67*o**6/40 + 1983*o**5/140 - 117*o**4/56 - 135*o**3/7 + 19*o**2 - 43*o. Express the second largest root of w(f) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Suppose -5*g - 12800 = -5*s, 4*s - 7680 = s + 2*g. Find the value of n + m, where n/m is the second largest root of 135 - 1344*f**3 - 26 - s*f**4 + 648*f**2 + 513*f - 28 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let r(m) be the first derivative of -10976*m**6/135 - 3724*m**5/15 - 1197*m**4/4 - 371*m**3/2 - 63*m**2 - 58*m + 80. Let i(s) be the first derivative of r(s). Suppose i(f) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let p(a) be the first derivative of -3744*a**5 + 3621*a**4 + 2200*a**3 - 3429*a**2/2 - 1080*a - 1627. Let p(n) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Let w(a) be the first derivative of 320*a**7/7 + 584*a**6/3 + 2081*a**5/6 + 2675*a**4/8 + 375*a**3/2 + 60*a**2 + 131. Let n(c) be the second derivative of w(c). Let n(l) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -924*c**2 + 216 - 1925*c**4 - 305*c + 2920*c**3 - 176*c + 135*c**2 + 5*c - 46*c, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of -9113*a - 3250/9*a**3 - 1716 + 26000/9*a**4 - 35035/3*a**2 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let n(b) = -97942*b**4 + 178096*b**3 - 118627*b**2 + 34200*b - 3578. Let z(x) = -244856*x**4 + 445240*x**3 - 296568*x**2 + 85500*x - 8944. Let q(f) = -28*n(f) + 11*z(f). For the polynomial q(g), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let l(j) be the second derivative of -168*j**6 + 3839*j**5/10 + 1385*j**4/12 - 5803*j**3/6 + 980*j**2 - 373*j. Express the second largest root of l(o) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let k be (-160380)/(-264)*(-29)/((-7975)/726). Suppose 51921/5*w**2 - 17820*w**4 - 3402/5 + k*w - 21888*w**3 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 81621/14*o**2 + 4131/14 + 660*o**4 - 4617/2*o - 70929/14*o**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let s(y) be the third derivative of -275*y**7/21 - 5*y**6/8 + 81*y**5/4 + 9*y**4/8 - 27*y**3/2 + 2123*y**2. Suppose s(f) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let t(r) be the second derivative of -508079*r**6/105 - 452023*r**5/70 - 24713*r**4/21 + 34528*r**3/21 + 6240*r**2/7 - 6*r - 38. Express the second largest root of t(c) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -3584/11*v**2 + 144/11 - 680*v**4 + 11124/11*v**3 - 204/11*v, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let s(r) be the third derivative of 55/2*r**7 - 16*r**2 + 3393/80*r**5 - 837/16*r**6 + 81/16*r**3 - 1215/64*r**4 + 1 + 0*r. For the polynomial s(m), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let j(b) be the third derivative of 7*b**10/216 + 283*b**9/864 + 1219*b**8/1120 + 257*b**7/140 + 9*b**6/5 + 11*b**5/5 - 2*b**2 + 5. Let u(k) be the third derivative of j(k). Express the second largest root of u(m) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "If 466422/7*a**2 + 55836/7 - 359766/7*a + 368852/7*a**3 + 19360/7*a**4 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let y(p) be the third derivative of 1700*p**7/27 - 18619*p**6/216 - 1459*p**5/36 + 235*p**4/3 + 40*p**3 + 459*p**2 - p + 2. For y(c) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let c(s) be the third derivative of 0*s - 231/20*s**5 + 539/15*s**7 - 297/8*s**4 + 0 - 149*s**2 - 297/14*s**3 + 1617/40*s**6. If c(o) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Suppose 14520*p**4 + 7600/7 - 70915/7*p**2 - 2080/7*p + 15730/7*p**3 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let t = 5458041/135002 + 4770/67501. If 2079*o**4 + t - 6579/10*o**2 - 3207/10*o**3 + 351/10*o = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 19200/13*u**4 + 3300/13 - 5920/13*u**3 + 17140/13*u - 33720/13*u**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let a be (37383/9 + 13)/(3/9 - -4). Express the second largest root of 30000/13*r**3 + 7425/13*r + 23625/13*r**2 + a*r**4 + 810/13 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let t(s) = 5899*s - 212960*s**4 + 1702 - 5949*s**2 + 4361*s - 137949*s**3 - 91. Let r(k) = 53240*k**4 + 34487*k**3 + 1487*k**2 - 2565*k - 403. Let p(w) = 9*r(w) + 2*t(w). Find the value of n + m, where n/m is the second largest root of p(z) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of -45760/9*l**4 - 21200/3*l**3 + 150*l - 315 + 5205*l**2 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Suppose -1303*s + 7818 = 2606*s. For the polynomial 3573/8*d**s - 5577*d**3 - 90 + 10647/2*d**4 + 528*d, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let p(k) be the first derivative of -50336*k**5/5 + 14311*k**4 + 43344*k**3 + 10350*k**2 - 16200*k - 1697. For the polynomial p(y), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Suppose -1140 = 52*n - 1296. For 0 - 1925/3*s**4 - 363*s**2 - 1705/2*s**n - 99/2*s = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let o(z) = -z**3 - z**2 + 1. Let s(g) = -g**4 - g**3 + g**2 + 2*g + 1. Let y(m) = 7747*m**4 - 5816*m**3 + 499*m**2 + 426*m - 73. Let h(q) = 3*s(q) + y(q). Let u(j) = -2*h(j) + 22*o(j). For u(b) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Suppose 14823/10 + 19065/2*s**3 + 1365*s**4 - 21357/10*s - 208521/10*s**2 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let f(l) be the third derivative of 2*l**2 - 1243/102*l**5 + 0*l + 240/17*l**3 + 520/51*l**7 - 150/17*l**4 + 0 + 593/68*l**6. Let f(c) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let l(x) be the first derivative of -16302*x**5 - 157613*x**4/2 - 30508*x**3 + 6512*x**2 + 4416*x - 5009. Express the second largest root of l(k) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let q(v) be the second derivative of 207*v**6 + 3033*v**5/20 - 8453*v**4/32 - 245*v**3/2 + 225*v**2 + 3*v + 205. Suppose q(i) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let t(f) be the third derivative of -53482*f**7/945 - 4994*f**6/45 - 12343*f**5/135 - 368*f**4/9 - 32*f**3/3 - 3124*f**2. Let t(k) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Suppose -5*l + 5*c + 10 = 0, 20 = 3*l - 59*c + 63*c. Express the second largest root of -1269/10*m + 3249/5*m**2 + 6909/10*m**3 - 1617*m**l - 324/5 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let c(n) be the first derivative of -486*n**5 + 21789*n**4/14 - 6626*n**3/7 - 4365*n**2/7 + 648*n - 1299. Express the second largest root of c(g) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let x(h) = -51450*h**4 + 67139*h**3 + 31001*h**2 - 12330*h - 3960. Let l(y) = 25725*y**4 - 33569*y**3 - 15501*y**2 + 6165*y + 1980. Suppose s = 37 - 33. Let q(t) = s*x(t) + 9*l(t). For q(d) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "If 624 - 11850*y**2 - 14316*y + 74022*y**3 + 2256 + 59319*y**4 - 435*y**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Suppose 2430/13 - 3996/13*a + 15216/13*a**3 + 40320/13*a**4 - 39384/13*a**2 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let t(q) = -61545*q**4 + 225792*q**3 - 280114*q**2 + 135569*q - 21053. Let g(x) = 20510*x**4 - 75264*x**3 + 93372*x**2 - 45190*x + 7018. Let u(y) = -7*g(y) - 2*t(y). Let u(p) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let s(r) be the second derivative of 504*r**6/17 - 65511*r**5/170 + 90413*r**4/68 - 45085*r**3/34 + 9594*r**2/17 + 7545*r. Suppose s(n) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let r(n) = n**4 + 2*n**3 + 2*n**2 + 1. Let q(j) = 41575*j**4 - 106726*j**3 - 147217*j**2 - 51435*j - 5405. Let m(g) = q(g) + 5*r(g). For the polynomial m(u), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let h(g) be the second derivative of 1881*g**6/8 - 35529*g**5/160 + 45*g**4/16 + 891*g**3/16 - 81*g**2/4 - 2*g + 204. Suppose h(y) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let u(c) be the third derivative of 135/2*c**3 - 219/2*c**5 + 0*c**6 + 0*c**4 + 3025/42*c**7 + 13 + 0*c + c**2. For the polynomial u(f), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -3571*i**2 + 4296*i**4 - 2910*i**3 + 1153*i**2 + 594*i + 648 + 703*i**2 + 429*i**4 - 2542*i**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let k(s) be the second derivative of -9504/7*s**6 + 6372/7*s**3 + 10 + s + 2430/7*s**2 + 5463/7*s**4 - 27954/35*s**5. For the polynomial k(l), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let x(s) = -3503*s**4 + 600*s**3 + 1215*s**2 - 51*s - 84. Let a(d) = -d**4 + d - 1. Suppose 2*v - 16 = -3*p - 3*v, -5*p = -4*v + 35. Let l(g) = p*a(g) + x(g). Express the second largest root of l(c) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let n(g) be the second derivative of -20020*g**6/9 - 29510*g**5/9 - 62023*g**4/54 + 4108*g**3/9 + 416*g**2 - 2*g + 103. Find the value of n + m, where n/m is the second largest root of n(p) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Suppose -43407/5*b**3 - 7938/5*b**4 + 2079 + 23763/5*b**2 + 41787/5*b = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let q(y) = 68 - 15*y. Let g be q(-11). Suppose g*z**2 + 1212*z**2 - 720 - 14735*z**3 + 3348*z - 468*z + 13475*z**4 - 945*z**3 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let t(w) be the third derivative of -120/7*w**3 + 0 + 0*w - 35/12*w**6 - 273*w**2 - 21/2*w**7 + 191/12*w**5 + 20/7*w**4. Let t(d) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let r(z) be the third derivative of -1625*z**9/3024 + 25*z**8/1152 + 4385*z**7/3024 - z**6/8 - 2*z**5 + 155*z**4/24 - z**2 + 22*z. Let w(x) be the second derivative of r(x). For w(f) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "If 17472*z**4 - 4756 + 6154*z - 7352*z**3 - 9428*z**2 + 2124*z + 3796 - 2070*z = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let m(h) be the first derivative of 429*h**7/14 - 277*h**6/15 - 779*h**5/20 + 75*h**4/4 + 36*h**3 - 14*h**2 + 64. Let v(b) be the second derivative of m(b). If v(y) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let l(i) be the third derivative of -8228*i**7/105 + 5159*i**6/75 + 5332*i**5/25 - 48*i**4 - 1152*i**3/5 - 1726*i**2. Express the second largest root of l(y) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Suppose -61200/7*c + 195925/7*c**3 - 1620 - 3975/7*c**2 + 22770*c**4 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let f(r) be the first derivative of 5236*r**6/27 - 2331*r**5/20 - 392*r**4/3 + 315*r**3/2 - 63*r**2 - 85*r - 156. Let g(z) be the first derivative of f(z). If g(d) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Let k = 1393 - 988. For the polynomial 243 + k*x - 1389*x**3 - 1581*x**2 - 1578*x**2 - 1140*x**3 + 9240*x**4, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let p(k) be the first derivative of 384*k**7/133 + 2872*k**6/285 + 4117*k**5/285 + 212*k**4/19 + 96*k**3/19 - 115*k**2/2 + 151. Let j(s) be the second derivative of p(s). Suppose j(u) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let c(f) be the first derivative of -45738*f**5/115 - 37851*f**4/46 - 7684*f**3/23 + 5544*f**2/23 + 3456*f/23 - 108. If c(g) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let f(c) be the second derivative of -440*c**6 - 12999*c**5/2 - 20433*c**4/4 + 9522*c**3 + 17577*c**2/2 - 405*c - 7. Suppose f(d) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let m(w) be the second derivative of 1 + 873/13*w**3 + 59*w - 35*w**6 + 648/13*w**2 - 1383/26*w**5 + 291/26*w**4. Find the value of n + m, where n/m is the second largest root of m(r) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 17253/17*i**3 + 71610/17*i**4 - 3645/17*i - 243/17 - 10719/17*i**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Suppose 6*k + 8*k = -378. Let j(n) = -10368*n**4 - 7204*n**3 + 5690*n**2 + 5117*n + 949. Let y(p) = -72576*p**4 - 50427*p**3 + 39831*p**2 + 35820*p + 6642. Let u(i) = k*j(i) + 4*y(i). Suppose u(c) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Suppose 27*l = 97*l - 240 - 40. For the polynomial -1800/11 + 17150/11*y**l + 8670/11*y - 13230/11*y**3 - 7910/11*y**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let g(i) be the third derivative of 114*i**2 + 0*i + 5645/24*i**6 + 630*i**3 + 0 + 1635/8*i**4 + 1700/21*i**7 - 1391/2*i**5. Suppose g(f) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let 44352/13 + 22176*x**4 - 753940/13*x**3 - 469700/13*x**2 + 63360/13*x = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let -2234 + 5805*q**2 + 1829 + 675*q - 1124*q**3 - 21560*q**4 - 3496*q**3 + 105*q**3 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "If -928*m**2 - 360 - 178*m**4 + 573*m - 524*m**3 - 1067*m**4 + 3459*m**2 - 1455*m**4 - 136*m**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose 2*c = 2*h - 1 + 3569, -25 = 5*h. Let -118 - 3691*o - c*o**2 - 314 + 315*o**2 + 847*o + 32032*o**4 + 20308*o**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let d(v) be the first derivative of -1232*v**5 - 2105*v**4/2 + 815*v**3 + 180*v**2 - 135*v - 292. If d(p) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let l = -282 - -333. Let n(s) = -174947*s**4 - 165119*s**3 - 25192*s**2 + 12161*s + 2897. Let y(k) = -21869*k**4 - 20640*k**3 - 3149*k**2 + 1520*k + 362. Let f(h) = l*y(h) - 6*n(h). If f(q) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Suppose -7 = 10*b - 37. Find the value of n + m, where n/m is the second largest root of -72733*m**b - 6228*m - 69212*m**4 - 33396*m**2 - 2360 + 1928 + 17111*m**3 - 23270*m**3 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let u(o) be the first derivative of 3640*o**5 - 6930*o**4 + 2814*o**3 + 6237*o**2/5 - 4536*o/5 - 522. Let u(y) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let r = 10419535/4 - 2591120. Let r*q**4 + 52437/8*q**3 - 567/8 - 3591/8*q**2 - 4725/8*q = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let i(m) be the second derivative of 2376*m**6/17 - 7281*m**5/170 - 7631*m**4/17 + 4833*m**3/17 + 6804*m**2/17 - m + 1747. For the polynomial i(h), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let i(r) be the third derivative of 343*r**7/6 - 637*r**6/120 - 3703*r**5/20 - 1401*r**4/8 - 36*r**3 + 1780*r**2. For the polynomial i(w), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Let l(r) be the third derivative of 135/4*r**5 + 0*r + 0 + 243/10*r**4 + 47*r**2 - 189/2*r**6 + 390/7*r**7 - 243/10*r**3. For l(z) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let j(h) be the third derivative of -299*h**7/16 - 1619*h**6/40 - 72*h**5/5 + 22*h**4 + 16*h**3 - 1120*h**2 - 2*h. Express the second largest root of j(f) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let d(r) = 4410*r**4 + 8764*r**3 - 6386*r**2 - 2900*r + 1580. Let g(m) = -4410*m**4 - 8764*m**3 + 6386*m**2 + 2896*m - 1579. Let y(t) = -5*d(t) - 4*g(t). Let y(x) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let t(q) = 28400*q**4 - 16489*q**3 - 19467*q**2 - 235*q + 1231. Let h be 5/7 + (-231)/49 + 1. Let i(m) = 9467*m**4 - 5496*m**3 - 6489*m**2 - 78*m + 411. Let r(z) = h*t(z) + 8*i(z). Express the second largest root of r(y) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Suppose -543*f - 16 + 1739 = 94. Let 729/10*r - 3567/5*r**f + 6399/10*r**2 - 3432*r**4 - 162/5 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let k(h) = -h**2 - 57*h + 1843. Let l be k(-80). Suppose -9/5*a**2 - 162/5 - 1917/10*a + 1815*a**4 + 2937/2*a**l = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let g(y) be the third derivative of -77*y**7/3 - 10703*y**6/480 + 19833*y**5/160 - 99*y**4/16 - 495*y**3/4 + 845*y**2. Suppose g(x) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Suppose 3*a = 6*a + 24. Let j(q) = -100328*q**4 + 8676*q**3 + 19926*q**2 - 802*q - 964. Let u(c) = -33443*c**4 + 2892*c**3 + 6642*c**2 - 267*c - 321. Let z(l) = a*u(l) + 3*j(l). Let z(h) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let d(b) = -35059*b**4 - 110965*b**3 - 12220*b**2 + 18935*b + 3969. Let u(t) = 7012*t**4 + 22193*t**3 + 2444*t**2 - 3787*t - 794. Let l(z) = -6*d(z) - 33*u(z). Let g(s) = 2104*s**4 + 6658*s**3 + 733*s**2 - 1136*s - 239. Let r(n) = -21*g(n) - 2*l(n). Find the value of n + m, where n/m is the second largest root of r(i) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "If -729*x - 92772*x**3 + 324 - 6660*x**2 + 993*x + 423*x + 2229*x - 125120*x**4 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Let q(i) be the second derivative of 3069*i**6/5 + 56667*i**5/20 + 41123*i**4/12 + 1801*i**3 + 468*i**2 + 663*i. Let q(g) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let f(w) be the third derivative of 4125*w**7/7 + 3485*w**6/24 - 12437*w**5/12 + 785*w**4/4 + 300*w**3 + 1474*w**2. Find the value of n + m, where n/m is the second largest root of f(k) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "If -16 - 11404*i**3 + 1126 + 2310 - 11318*i**3 + 11760*i**4 + 8763*i - 16665*i**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let g = 25095 - 13153. Express the second largest root of -42084*y + 5616 - g*y**4 + 34135*y**4 + 15292*y**4 - 115689*y**3 + 110316*y**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let s(f) be the first derivative of -18018*f**5/19 - 602435*f**4/38 + 384620*f**3/19 + 482840*f**2/19 + 153600*f/19 - 320. Let s(g) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Suppose -6*t + 1094 = 206. Let 3046*r**2 - 158*r - 8190*r**4 - t*r + 346*r**3 - 216 + 200*r**2 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let u(d) = -700*d**4 + 2460*d**3 - 2531*d**2 + 843*d - 84. Let z(v) = 7700*v**4 - 27060*v**3 + 27840*v**2 - 9275*v + 925. Let t(x) = -x - 68. Let g be t(-3). Let j(s) = g*u(s) - 6*z(s). Express the second largest root of j(w) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let y(u) be the third derivative of 0*u + 113*u**2 + 21329/300*u**5 + 2261/20*u**4 - 14*u**7 + 0 + 147/2*u**3 - 119/30*u**6. Let y(n) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let b(g) = 4820*g + 43384. Let l be b(-9). Express the second largest root of -243 - 648/5*n - 68607/5*n**l + 8712/5*n**3 + 21438/5*n**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "If 6732*c**4 + 271596*c**2 - 28123*c**3 - 218079*c - 3058504 + 2978314 - 17204*c**4 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let 3825*k**4 + 770*k**3 - 610*k - 21760/9*k**2 + 175 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of 11904 - 34222*n**3 - 5036*n**2 + 35377*n**2 + 87*n**2 - 28750*n**3 - 12936*n**4 + 56368*n = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let m(f) be the first derivative of -16335*f**5/14 + 105699*f**4/56 - 11555*f**3/14 + 477*f**2/28 + 54*f - 1793. Let m(o) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Suppose -2772 + 17418*k**3 - 3500*k**4 - 1629*k + 10323*k**2 - 12318*k**3 - 1708*k**2 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -3270 + 7944*p + 2821*p**4 - 6853*p**4 - 591 - 5584*p**3 + 8933*p**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "If 405/8 + 1881*w**2 + 2619/4*w - 34125/8*w**4 - 4035/4*w**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Let p(v) be the second derivative of 4928*v**6/5 - 1929*v**5/20 - 2931*v**4/4 + 93*v**3/2 + 639*v**2/2 + 20*v - 1. Let n(x) = 14784*x**4 - 964*x**3 - 4395*x**2 + 139*x + 320. Let c(g) = -9*n(g) + 4*p(g). Express the second largest root of c(z) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 2626*o - 39985*o**3 - 567 + 15379*o**4 + 1324*o + 14635*o**3 - 1775*o**2 + 371*o**2 - 8*o = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "If 17930*c**2 - 1529*c**3 - 1399 - 806 - 11025*c + 32640*c**4 + 61689*c**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let y(o) be the third derivative of -325*o**8/1064 - 435*o**7/1064 + 45*o**6/152 + 351*o**5/760 - 81*o**4/152 - 253*o**3/6 - 222*o**2. Let x(t) be the first derivative of y(t). For the polynomial x(m), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let h(o) = 10778*o**4 + 30970*o**3 + 31058*o**2 + 13174*o + 2022. Let w(x) = x**4 - x**3 + x**2 + x - 3. Let v(l) = -h(l) - 2*w(l). Let v(f) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Suppose -5*l - 266 = -306. Express the second largest root of -99 - 111 - l*n + 2781*n**2 - 1 - 29 - 916*n**3 - 4620*n**4 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of 1728/11*l - 9399/11*l**3 + 567/22 - 14280/11*l**4 + 2151/22*l**2 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For -1728 - 79044*t**2 + 2008*t**4 - 19149*t - 921*t - 23521*t**4 - 4227*t**4 - 112202*t**3 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let p(c) = -51565*c**4 + 75734*c**3 - 19195*c**2 - 13582*c + 5408. Let d(b) = 17187*b**4 - 25245*b**3 + 6399*b**2 + 4527*b - 1803. Let z(i) = 8*d(i) + 3*p(i). Find the value of n + m, where n/m is the second largest root of z(w) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let o(l) be the first derivative of -3080*l**6/3 - 689*l**5/2 + 2985*l**4/4 + 225*l**3/2 - 270*l**2 - 53*l - 63. Let b(a) be the first derivative of o(a). For b(v) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let a(x) be the first derivative of 2800*x**5 - 20175*x**4/4 + 2655*x**3 + 135*x**2/2 - 405*x + 1561. For the polynomial a(g), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let i(t) = 6160*t**2 - 4*t - 8. Let o be i(-2). Let 14 + 298 + 12 - 2376*y - o*y**4 + 2700*y**2 + 12792*y**3 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let w(c) be the third derivative of 21*c**2 + 520/21*c**7 + 561/5*c**5 - 333/4*c**4 - 979/12*c**6 + 36*c**3 + 2*c + 0. For w(m) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Suppose -12 = 279*y - 285*y. Express the second largest root of 6160*k**4 - 299*k**3 + 51 - 73*k**3 - 54*k**3 + 111 - 2322*k**y - 54*k = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let t be (-1042)/(-16) - (-21658)/(-784). For the polynomial -5775*a**4 - t*a + 1570*a**2 + 1495/6*a**3 - 90, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose 567/10 + 46950*b**3 + 45045/2*b**2 + 3348*b + 23250*b**4 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let y be 2 - 9736/(-55) - ((-5040)/(-231) - 21). For -7260*l**3 - 15400*l**4 + 1782*l**2 + y + 6831/5*l = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let n(w) = 111982*w**4 + 26151*w**3 - 33057*w**2 - 4104*w + 2601. Let y(s) = 55992*s**4 + 13076*s**3 - 16528*s**2 - 2052*s + 1300. Let p(a) = -4*n(a) + 9*y(a). Suppose p(k) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose 1701/23 - 13500/23*u**4 + 8505/23*u**2 + 10500/23*u**3 - 8802/23*u = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let u(d) be the second derivative of -256*d**6/3 + 2672*d**5/5 + 670*d**4 - 501*d**3/2 - 540*d**2 + 4012*d. Suppose u(x) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let m(v) be the second derivative of 315*v**6 + 16509*v**5/4 + 71513*v**4/12 + 3420*v**3 + 936*v**2 + 18*v + 34. Express the second largest root of m(n) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let g be (14/(-140))/((-11)/(66825/10)). Suppose -1050*w**4 + g - 4293/8*w**2 - 6435/4*w**3 + 1053/8*w = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "If -9747/7*y + 108000/7*y**4 + 103500/7*y**3 + 4212/7 - 8280*y**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let c = 167667193/119288 - -6803/9176. For the polynomial -3546/13*m**2 + 2538/13*m + 810/13 - 15120/13*m**4 - c*m**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let p(h) be the first derivative of -2706*h**5 + 1030207*h**4/28 + 112463*h**3 + 218817*h**2/14 - 36531*h + 9685. For the polynomial p(n), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let y(r) = 18816*r**4 - 199301*r**3 + 497950*r**2 - 249675*r + 30594. Let c(w) = -94080*w**4 + 996504*w**3 - 2489748*w**2 + 1248372*w - 152968. Let b(s) = -3*c(s) - 16*y(s). Find the value of n + m, where n/m is the second largest root of b(f) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Let g(k) = -16339*k**4 - 22143*k**3 - 6041*k**2 + 1643*k + 540. Let v(c) = -16338*c**4 - 22143*c**3 - 6042*c**2 + 1644*c + 540. Let b(o) = -3*g(o) + 4*v(o). Express the second largest root of b(u) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let t be (-243)/((-1 + -65)/((-3)/2))*(-269760)/2810. For the polynomial -1296/11 - 1512*p**3 + t*p - 2304/11*p**2 + 15680/11*p**4, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 5790*y + 846/5*y**3 - 2520 - 4752*y**4 + 70089/5*y**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let b(f) be the first derivative of -4032/5*f**5 - 4663/3*f**3 + 672*f**2 - 295 - 144*f + 1780*f**4. For the polynomial b(u), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let p(b) be the third derivative of 45/4*b**3 + 0 - 1001/24*b**6 + 108*b**2 - 3/8*b**5 + 75/4*b**4 + 0*b - 2420/63*b**7. For p(h) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let b(w) = -w**3 - 103*w**2 + 4489*w + 138. Let d be b(-136). Suppose 81/2*a + 243/20 - 528*a**4 - 2349/20*a**d - 2844/5*a**3 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let n(y) be the third derivative of 4000*y**7/21 - 775*y**6/3 - 175*y**5/2 + 1515*y**4/8 + 225*y**3/2 - 452*y**2. Suppose n(s) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let a(v) be the first derivative of 2 + 63*v**3 + 1605/4*v**4 + 280*v**5 - 297/2*v**2 - 81*v. If a(b) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let m(q) be the third derivative of 128/45*q**7 - 21*q**2 + 0*q + 64/75*q**6 - 2 + 18/5*q**3 - 3/5*q**4 - 99/25*q**5. Find the value of n + m, where n/m is the second largest root of m(v) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let m(x) = 4760*x**4 + 11559*x**3 + 5469*x**2 + 27*x - 243. Let d(h) = -15 - 13 + 43 - 15 - h**3 - h**2. Let k(f) = -6*d(f) - m(f). For the polynomial k(p), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 1368/5 + 10164/5*l**4 + 2692/5*l**2 + 7788/5*l - 73876/15*l**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose -720 - 195696*s**4 + 3732*s - 19072*s**3 - 182*s**2 + 217584*s**4 - 576*s**2 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let u(c) = -1162752*c**4 + 360652*c**3 + 138724*c**2 - 52336*c + 2912. Let a(r) = 232550*r**4 - 72130*r**3 - 27745*r**2 + 10467*r - 582. Let w(m) = -16*a(m) - 3*u(m). Suppose w(x) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Let m(n) = 117030*n**4 + 188040*n**3 + 108415*n**2 + 26855*n + 2440. Let k(d) = d**4 - 3*d**3 - d**2 + d - 1. Let u(c) = 10*k(c) + m(c). Let u(x) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let v be ((-15903)/(-10) - 12/40)/(52/65). Let -3500/3*s**4 - 135/4 - v*s**3 - 675/2*s - 4965/4*s**2 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let i(h) be the first derivative of -1176/5*h**5 - 35 - 243/5*h - 2439/5*h**3 - 10773/20*h**4 - 2187/10*h**2. For i(y) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let z(f) = -10448*f**4 + 18986*f**3 + 19167*f**2 + 5320*f + 465. Let j(s) = -2*s**4 - s**3 - s**2 - s + 3. Let c(q) = -2*j(q) - 2*z(q). Suppose c(b) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -1845*h**3 - 22464/5 - 94392/5*h - 105558/5*h**2 + 2835*h**4, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let r(i) = 3*i**3 - 310*i**2 + 129*i - 2674. Let d be r(103). If 30800/13*v**d + 44490/13*v**3 - 6345/13*v + 7425/13*v**2 - 1620/13 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let d(b) be the first derivative of 3168*b**5 - 4725*b**4/2 - 16311*b**3/5 + 13797*b**2/5 - 648*b - 2004. If d(c) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let d(x) be the second derivative of -590*x**4 - 225*x**6 + 872*x**2 - 59*x + 3979*x**4 + 2544*x**3 - 755*x**6 - 43*x + 1057*x**5 - 8*x**2. Let d(b) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let d(t) = 12796*t**4 - 1911*t**3 - 2825*t**2 + 233*t + 145. Let o(p) = 6398*p**4 - 956*p**3 - 1412*p**2 + 116*p + 73. Let u(a) = 6*d(a) - 13*o(a). Let r(v) = -31989*v**4 + 4811*v**3 + 7031*v**2 - 551*v - 394. Let k(m) = -2*r(m) + 11*u(m). For the polynomial k(s), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let c(k) be the first derivative of -18711*k**5 - 36315*k**4/2 + 2360*k**3 + 8240*k**2 + 3200*k + 47. For c(u) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let -2352*u**4 + 3267/5*u**2 - 4914/5*u**3 + 1944/5*u + 243/5 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let n(c) be the second derivative of -243/2*c**2 + 11264/5*c**6 + 2*c + 8064/5*c**5 - 783/2*c**3 - 11 - 162*c**4. For the polynomial n(b), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of 7323/8*c**2 + 59115/8*c**3 - 7425/8 + 3675/4*c**4 - 27675/8*c = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "If 32940/23*y + 69066/23*y**2 - 73920/23*y**4 + 3402/23 - 6648/23*y**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let z(m) = 252000*m**4 + 13445*m**3 - 63180*m**2 - 1215*m + 3535. Let j(y) be the third derivative of -400*y**7/3 - 249*y**6/20 + 117*y**5 + 45*y**4/8 - 131*y**3/2 - 93*y**2. Let b(d) = 55*j(d) + 6*z(d). Find the value of n + m, where n/m is the second largest root of b(i) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let y(s) be the first derivative of -29040/7*s**5 + 7 + 1215/7*s + 6435/2*s**4 - 4050/7*s**2 - 135/7*s**3. Find the value of n + m, where n/m is the second largest root of y(q) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -2079/16 - 2223/16*j - 26865/16*j**3 + 975/2*j**4 + 22791/16*j**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Suppose 72501/8*o**4 + 9477/16*o**2 - 1377/16*o + 80613/16*o**3 - 243/16 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let c(i) = 2*i**3 + 50*i**2 + 282*i - 92. Let b be c(-16). If 1296/23*s**2 - 486/23 - 8820/23*s**3 + 1620/23*s + 7350/23*s**b = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Suppose -378 + 45619/8*r**4 + 8085/8*r**2 + 6860*r**3 - 1260*r = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let s(y) = -32169*y**4 - 2774*y**3 + 12678*y**2 + 528*y - 669. Suppose 18*o + 66 = -42. Let u(x) = -450365*x**4 - 38835*x**3 + 177490*x**2 + 7390*x - 9365. Let v(n) = o*u(n) + 85*s(n). If v(g) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let x(n) be the third derivative of -8*n**10/675 + 268*n**9/12285 + 17*n**8/21840 - 67*n**7/1820 + 3*n**6/65 + n**5/5 - 23*n**2. Let h(q) be the third derivative of x(q). Find the value of n + m, where n/m is the second largest root of h(m) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let l be 4873 + 13/(91/(-14)). Express the second largest root of -797*r - 3028*r - l*r**2 - 5141*r**2 + 1620 - 683*r**2 + 24640*r**4 + 15760*r**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Suppose 55440*o**4 + 4599/5*o - 97111/5*o**3 + 189 - 8589*o**2 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let d(x) = 5003*x**4 - 17956*x**3 + 19676*x**2 - 6804*x + 729. Let w(g) = 20011*g**4 - 71820*g**3 + 78705*g**2 - 27216*g + 2916. Let y(q) = 9*d(q) - 2*w(q). For the polynomial y(p), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let a(q) be the third derivative of -198/17*q**3 + 0 - 89*q**2 + 0*q - 399/34*q**4 + 4693/510*q**6 + 371/85*q**5 - 176/51*q**7. Suppose a(g) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let z(m) be the third derivative of 1267/570*m**6 + 388/95*m**5 + 112/285*m**7 + 36/19*m**3 + 141/38*m**4 + 0 + 0*m + 211*m**2. If z(c) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let i(r) be the first derivative of 14014*r**5/3 - 10829*r**4/2 - 201877*r**3/18 - 11739*r**2/2 - 2535*r/2 + 1980. Express the second largest root of i(g) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial -4560*r**4 + 42918/11*r**3 + 648/11 + 3708/11*r**2 - 5562/11*r, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of -4459/10*r**3 + 3087*r**4 + 819/10*r + 378/5 - 4893/5*r**2 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Suppose 18629*d**2 + 34346*d**4 + 922*d**4 - 2290 - 317760*d**3 + 42200*d + 10492*d**4 + 72016*d**2 - 10430 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let b(g) be the first derivative of -6050/3*g**2 + 20975/27*g**3 + 800*g - 54 + 33625/12*g**4 - 22750/9*g**5. Find the value of n + m, where n/m is the second largest root of b(p) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let z(x) be the third derivative of 9*x**8/16 - 1993*x**7/2240 - 503*x**6/960 + 9*x**5/4 - 9*x**4/4 - 7*x**3/6 + 26*x**2 - x. Let d(w) be the first derivative of z(w). Express the second largest root of d(o) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let w(z) = -85800*z**4 + 76028*z**3 + 35822*z**2 - 6870*z - 2544. Let a(s) = -1526 - 815*s**3 + 46432*s**3 - 51480*s**4 - 4122*s + 15862*s**2 + 5631*s**2. Let t(k) = -12*a(k) + 7*w(k). Let t(c) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let -324/5 + 1872/5*q**2 - 2133/5*q + 5667*q**3 + 6930*q**4 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -630*p**2 + 17160/7*p**4 + 11379/7*p**3 - 4077/7*p - 648/7 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Suppose 5*d + 3539 = 8*d + j, 0 = -2*d - 4*j + 2376. For the polynomial 29 + d*l**4 + 183*l**4 - 68*l**4 + 2575*l**3 - 137 + 457*l**4 - 189*l + 900*l**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Let w(n) be the third derivative of -699/10*n**5 + 0*n**4 + 0*n + 0 + 63/5*n**6 - 224*n**2 + 27*n**3 + 308/3*n**7. Express the second largest root of w(p) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let q = 904426374/101 - 9948515586/1111. For q - 14760/11*f + 22950/11*f**4 + 44058/11*f**2 - 53745/11*f**3 = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let w(h) be the third derivative of -442*h**7/3 + 14419*h**6/60 - 901*h**5/15 - 108*h**4 + 96*h**3 - 2*h**2 + 404*h - 3. For w(c) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Let j(m) be the second derivative of 90*m**7/23 - 275*m**6/46 - 267*m**5/115 + 495*m**4/46 - 216*m**3/23 - 231*m**2/2 + 11*m + 1. Let r(s) be the first derivative of j(s). If r(f) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let r(f) = -147940*f**4 + 185420*f**3 + 119415*f**2 - 2045*f - 4840. Let z(j) = -49315*j**4 + 61807*j**3 + 39804*j**2 - 682*j - 1613. Let t(q) = 7*r(q) - 20*z(q). If t(n) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let b(i) be the second derivative of -143*i**7/28 + 453*i**6/35 - 2327*i**5/280 - 153*i**4/28 + 72*i**3/7 - 27*i**2/2 - 6*i - 1. Let g(j) be the first derivative of b(j). If g(y) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let m(d) be the first derivative of -38220*d**5/11 - 2905*d**4 + 7028*d**3/11 + 11214*d**2/11 + 3024*d/11 + 294. Let m(g) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let x(y) be the first derivative of -2340*y**2 + 3815/2*y**4 - 2525*y**3 - 9 + 3920*y**5 - 675*y. For x(r) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let m = -34652 + 34688. For the polynomial 120*v - 348*v**2 - 14080/9*v**4 - 5056/3*v**3 + m, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let z(c) = -c**4 + 5*c**2 - 1. Let i(x) = 4502*x**4 + 8608*x**3 + 2392*x**2 - 1620*x - 572. Let l(w) = -2*i(w) - 44*z(w). If l(y) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "If 29681*q**4 + 2627 + 45972*q**3 - 3463*q**2 + 733 + 19823*q**4 - 14465*q + 2569*q - 12197*q**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of -126*v**2 + 11670*v**4 - 17424*v**3 + 416*v + 880*v - 162 + 19306*v**4 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let w(k) = 1010*k**4 + 2180*k**3 + 1750*k**2 + 621*k + 81. Let b(r) = 1012*r**4 + 2186*r**3 + 1744*r**2 + 616*r + 76. Let f(n) = 1012*n**4 + 2187*n**3 + 1743*n**2 + 615*n + 75. Let o(z) = -6*b(z) + 5*f(z). Let d(u) = 5*o(u) + 6*w(u). Let d(a) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 17100*a**4 + 23931/8*a**2 - 1053/2 + 184545/4*a**3 - 30051/8*a, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let w(i) be the first derivative of -637*i**5 - 10423/8*i**4 - 8001/20*i**2 - 378/5*i + 8 - 5173/5*i**3. Express the second largest root of w(h) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let n(p) be the third derivative of 55*p**8/6 + 967*p**7/42 + 63*p**6/5 - 117*p**5/10 - 18*p**4 + 59*p**3/6 + 6*p**2 + 4. Let b(d) be the first derivative of n(d). If b(t) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 183*t + 3070*t**3 - 1760 - 14634*t**3 - 2688*t**4 + 3449*t + 8810*t**2 - 7014*t**4 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let b(s) be the third derivative of 275*s**8/96 + 475*s**7/84 + 269*s**6/192 - 57*s**5/16 - 225*s**4/64 - 149*s**3/6 - 106*s**2. Let d(z) be the first derivative of b(z). For d(q) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let u(t) be the second derivative of -2288*t**7/15 + 1853*t**6/30 + 2333*t**5/15 - 32*t**4 - 96*t**3 - 12*t**2 - t - 6. Let z(w) be the first derivative of u(w). Express the second largest root of z(p) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let g(r) be the first derivative of 416*r**5 - 8083*r**4/9 + 20500*r**3/27 - 944*r**2/3 + 64*r + 406. If g(y) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 5602*k**2 + 4900*k**4 - 908*k**3 - 6453*k**3 + 5*k + 697*k - 630 - 3629*k**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Let d be (-5)/((-135)/(-126))*(-762)/4. Express the second largest root of 551*o - 441*o**2 + 97*o - 81 + d*o**3 - 5659*o**3 + 6800*o**4 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let d(c) be the second derivative of 71874*c**6/13 - 3769029*c**5/65 - 755700*c**4/13 - 146208*c**3/13 + 58752*c**2/13 - c - 530. For the polynomial d(r), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Let u(p) be the second derivative of -605*p**6/2 + 1419*p**5/2 - 273*p**4/4 - 900*p**3 + 648*p**2 + 133*p. Express the second largest root of u(m) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let r(l) be the first derivative of 8624*l**5/5 - 8575*l**4/2 + 2076*l**3 + 1161*l**2 - 1080*l - 264. Express the second largest root of r(w) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let 10962*y**2 - 4891*y**4 - 50*y**3 + 1428 + 12181*y**3 + 601*y**4 - 9311*y = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let h(q) be the second derivative of -3773*q**6/3 + 6419*q**5/4 + 595*q**4/4 - 1965*q**3/2 + 945*q**2/2 - 43*q + 2. Let h(z) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -12870*t**4 - 2899*t**2 + 21999*t**3 + 4104*t + 17296*t**2 + 4044*t**2 - 3744 - 14700*t = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Let k(q) be the second derivative of 440*q**6/3 - 6093*q**5/2 + 21393*q**4/2 - 10737*q**3 + 4617*q**2 - 1584*q. Suppose k(j) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let g(r) be the third derivative of 13*r**2 - 243/38*r**3 - 435/76*r**6 + 0 + 189/38*r**4 - 40/19*r**7 + 1737/380*r**5 + r. Express the second largest root of g(y) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "If -15379*m**4 - 155168/9*m - 433147/9*m**3 - 137852/3*m**2 - 6656/3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -3410*i**2 + 103 + 371 + 17640*i**4 + 246 + 30288*i**2 - 7578*i - 37352*i**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Let h = -372639 - -1869189/5. Suppose 14436/5*j**3 - h*j + 243/2 + 5805/2*j**2 - 12474*j**4 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let v(f) = f**4 - f**3 - f**2 - f. Let b(d) = 12317*d**4 - 16953*d**3 + 8661*d**2 - 1941*d + 162. Let o = -90 + 88. Let u(m) = o*b(m) - 6*v(m). Let u(t) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let w(h) be the first derivative of 0*h - 18 + 81/28*h**2 - 27/14*h**3 + 231/10*h**5 - 135/8*h**4. Suppose w(b) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Let -1836*y + 6912*y**4 - 65428*y**3 + 185214 - 24336*y**2 - 58942*y**4 + 185401 - 370345 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let d(u) = 3*u**4 - u**3 - u**2 - 2*u + 1. Let m(s) be the first derivative of 11064*s**5/5 + 6797*s**4/2 - 5446*s**3/3 - 1153*s**2 + 694*s - 83. Let o(g) = -8*d(g) - m(g). Let o(v) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let y(q) = 113461 - 28048*q. Let c be y(4). Let 2214*i + 1512/5 - 4290*i**4 + 20127/5*i**2 - c*i**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let k(z) = -9000*z**4 - 15125*z**3 - 2397*z**2 + 5463*z + 2037. Let g(t) = 99000*t**4 + 166375*t**3 + 26365*t**2 - 60090*t - 22405. Let h(i) = 6*g(i) + 65*k(i). Express the second largest root of h(l) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Suppose -2130*v**2 + 11960/7*v - 25125/7*v**3 + 4800/7 + 17875/7*v**4 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Let z(r) be the second derivative of -23296*r**6/15 - 17832*r**5/5 - 2237*r**4 + 1103*r**3/3 + 780*r**2 + 9*r + 103. For the polynomial z(n), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let h(n) be the first derivative of -77*n**8/15 + 111*n**7/20 + 73*n**6/40 - 27*n**5/5 + 27*n**4/8 - 20*n**3/3 + 43. Let m(s) be the third derivative of h(s). Let m(d) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let h(r) be the second derivative of 209*r**7/14 + 7839*r**6/280 + 45*r**5/4 - 81*r**4/8 - 81*r**3/7 - 10*r**2 + 30*r. Let x(f) be the first derivative of h(f). For x(y) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of 6728*d**3 - 2349*d**2 + 381*d**2 + 540 + 29000*d**3 - 712*d - 47040*d**4 - 2564*d = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let k(s) be the second derivative of -8192*s**7/875 + 2688*s**6/125 - 2592*s**5/125 + 54*s**4/5 - 81*s**3/25 - 60*s**2 - 40*s + 3. Let f(z) be the first derivative of k(z). Let f(i) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -3085 + 16494*g - 101959*g**2 - 10465*g**4 + 20358*g - 6475*g**4 - 1091 + 92972*g**3 - 1117*g**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Let x(f) be the first derivative of 114 - 363*f**5 + 621/16*f**2 - 81/2*f + 735/4*f**3 - 4587/32*f**4. If x(h) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let g(f) be the first derivative of 663*f**6/2 - 33133*f**5/35 + 88757*f**4/84 - 4148*f**3/7 + 1224*f**2/7 + 19*f - 60. Let d(x) be the first derivative of g(x). For the polynomial d(m), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let v(y) be the first derivative of -858*y**5 - 1008*y**4 + 130*y**3/11 + 2808*y**2/11 + 864*y/11 - 916. Let v(x) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let d(o) be the first derivative of -55*o**8/208 - 435*o**7/728 + 81*o**6/520 + 783*o**5/520 + 81*o**4/52 - 28*o**3/3 + 6. Let x(y) be the third derivative of d(y). For x(b) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let w(y) be the third derivative of 0*y - 3077/16*y**4 - 76*y**2 + 69377/360*y**5 + 85*y**3 - 2431/21*y**7 + 0 + 1717/180*y**6. Express the second largest root of w(f) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let v = -212 - -216. Let -8896*x**2 - 17754*x**4 - 13389*x**2 + 3894*x**v + 840*x - 34500*x**3 + 2205 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let -7788*y - 72397*y**3 + 891 + 786*y + 4928*y**4 + 17823*y**2 + 55917*y**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let t(s) be the first derivative of 2931/4*s**4 - 243/2*s**2 + 2714*s**3 - 4914*s**5 - 43 - 540*s. Suppose t(n) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let f(d) = -7334*d**4 - 25313*d**3 - 29261*d**2 - 12736*d - 1612. Let c(l) = 4890*l**4 + 16875*l**3 + 19508*l**2 + 8491*l + 1075. Let n(h) = 8*c(h) + 5*f(h). Let n(k) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Let v(k) be the first derivative of -3762*k**5/5 + 4269*k**4/10 + 5081*k**3/10 - 747*k**2/10 - 108*k - 5010. If v(i) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Suppose -33480/7 - 20520/7*u - 295275/7*u**3 + 83355/2*u**2 + 70125/14*u**4 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Suppose -6372/5*x**2 + 108 + 344*x**3 - 432/5*x + 2880*x**4 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let l(y) be the first derivative of 30000*y**5/11 - 277875*y**4/22 + 6300*y**3/11 + 66015*y**2/11 + 14580*y/11 - 387. Find the value of n + m, where n/m is the second largest root of l(c) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 13392*s - 66836*s**4 - 4464/5 + 575484/5*s**3 - 323237/5*s**2, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "If 42442*t**3 + 83537*t**3 - 37235*t + 19328*t**4 - 806*t**4 - 9451*t + 35637*t**2 - 10440 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -864/7 + 3904/7*c**3 + 72*c - 168960/7*c**4 + 27096/7*c**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Let l(d) be the third derivative of -819/220*d**5 + 315/44*d**4 + 0 + 189/22*d**3 + 30*d**2 + 2*d - 112/11*d**6 - 160/33*d**7. If l(w) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let o(v) be the third derivative of 11*v**8/14 + 8457*v**7/3640 + 297*v**6/104 + 999*v**5/520 + 81*v**4/104 - 32*v**3/3 - 26*v**2. Let y(a) be the first derivative of o(a). If y(z) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let f be 171/(224523/(-1010)) - (186/13)/(-3). Express the second largest root of -4875*p**f - 10975/6*p**3 + 1365*p**2 + 90 + 1485/2*p = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let j(l) be the first derivative of 121*l**8/12 + 2288*l**7/105 + 581*l**6/90 - 104*l**5/5 - 24*l**4 + 206*l**3/3 - 256. Let c(m) be the third derivative of j(m). Express the second largest root of c(w) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let i(o) = -6*o**3 - 160*o**2 - 15*o - 1859. Let t be i(-27). Suppose 4576*r**t + 4300*r**3 - 540/11 - 2484/11*r + 7308/11*r**2 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the polynomial 185289*w**3 + 78359*w**2 + 256813*w**2 + 179035*w**3 + 440331*w**4 + 11040 + 106376*w - 392283*w**4, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of 18858/5*l**2 - 3185*l**4 - 504*l - 945 + 1400*l**3 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let b(q) = -q**4 - 2*q**3 - 3*q**2 + 1. Let t(p) = 11472*p**4 - 14776*p**3 + 4922*p**2 + 120*p - 141. Let d(r) = -3*b(r) + t(r). Suppose d(u) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Let p(h) be the first derivative of 21 + 891/10*h**2 + 1210*h**5 + 891/10*h - 1023/2*h**3 - 495*h**4. Let p(v) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let b(k) be the second derivative of -675*k**6 - 11745*k**5/4 - 16245*k**4/4 - 749*k**3 + 2940*k**2 - 15*k - 4. If b(s) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 1690 + 33600*v**4 - 2830*v + 1586 + 35440*v**3 + 1604*v**2 - 15460*v**2 - 8030*v = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let 67093*g**3 - 14963*g**2 + 2078 - 4334*g**2 - 638 - 2027*g + 32955*g**4 - 3765*g**2 - 2869*g = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let b(d) be the third derivative of 27*d**3 + 88/3*d**7 + 0*d - 92*d**2 + 0 - 307/20*d**6 + 99/8*d**4 - 639/20*d**5. For b(l) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Suppose -45 = 2*k - 7*p, k + 66*p - 65*p - 9 = 0. If -6175*j**4 - 6705/8*j**k + 48565/8*j**3 - 2295/4*j + 135 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let 93 - 83 + 2286*u - 1974*u**3 + 120 - 9000*u**4 + 140 - 4376*u**3 + 2490*u**2 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Let a be ((-2)/(-1) + 53)*1. Let k(c) = -330805*c**4 + 212680*c**3 + 136810*c**2 - 51840*c - 19385. Let o(f) = 12252*f**4 - 7877*f**3 - 5067*f**2 + 1920*f + 718. Let b(m) = a*o(m) + 2*k(m). If b(y) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "If 1658*w**4 + 48872*w**2 + 45598*w**2 + 14352 + 4516*w**4 - 16252*w**2 - 60350*w - 38906*w**3 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 398110/9*x**2 + 13650*x**4 + 16650*x + 134770/3*x**3 + 2000 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Let 78806*b**4 + 54443*b**3 - 16920*b - 2880 + 31312*b**3 - 2382*b**2 - 7348*b**2 + 44044*b**4 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let r(y) be the first derivative of 54*y + 11367/40*y**4 - 208*y**3 - 1611/20*y**2 + 12012/25*y**5 - 28. Suppose r(g) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let h(f) be the second derivative of 0 - 1089/5*f**5 - 11011/50*f**6 - 27/2*f**4 + 243/10*f**2 + 54*f**3 + 26*f. Find the value of n + m, where n/m is the second largest root of h(a) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let d(i) be the third derivative of -16 + 117/8*i**3 - 1305/128*i**4 + 27/14*i**7 + 0*i - 3*i**2 + 2103/320*i**6 - 1729/320*i**5. Let d(c) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let f = 38425 - 26310. For the polynomial 13913*q**3 - f*q**3 - 21276*q**2 - 34963*q**3 - 5808*q - 576 - 18150*q**4, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let h(k) be the second derivative of 275*k**6/7 + 765*k**5/14 + 675*k**4/56 - 27*k**3/2 - 243*k**2/28 + k + 164. If h(z) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Suppose 48 = 8*n + 16*n. Express the second largest root of 28662*q**4 + 810*q + 8827*q**4 + 324 - 309*q**4 - 6768*q**n - 9594*q**3 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let t(a) = -84*a**2 + 933*a - 95. Let k be t(11). Express the second largest root of -252*b**3 - 6006*b**k + 324/7*b - 486/7 + 10368/7*b**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let u(b) be the second derivative of -24*b**8/7 - 382*b**7/35 - 329*b**6/45 + 23*b**5/2 + 75*b**4/4 + 6*b**3 - 5*b. Let z(n) be the second derivative of u(n). Express the second largest root of z(o) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let u(r) = -10643*r**4 + 25758*r**3 - 2491*r**2 - 5344*r + 1084. Let w(x) = 10641*x**4 - 25754*x**3 + 2490*x**2 + 5343*x - 1086. Let n(v) = 3*u(v) + 2*w(v). If n(b) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let x(c) = -40247*c**4 - 49198*c**3 - 7695*c**2 + 7791*c + 2025. Let m(k) = -k**4 - 9*k**3 - 2*k. Let q(j) = 3*m(j) + x(j). Find the value of n + m, where n/m is the second largest root of q(p) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let l(t) = t + 2. Let w be l(2). Suppose -196*i**w - 509*i**3 - 5804*i**4 + 3465*i**2 + 91 - 1141*i**3 + 351*i - 415 = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let s(v) = 422*v**5 - 13*v**4 - 477*v**3 + 324*v**2 - 79*v + 32. Let c(h) = -845*h**5 + 25*h**4 + 954*h**3 - 648*h**2 + 157*h - 65. Let w(u) = 2*c(u) + 5*s(u). Let r(p) be the first derivative of w(p). Find the value of n + m, where n/m is the second largest root of r(z) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let r be 485 - (-4 - 2 - 2/(-1)). If -19250*s**4 + 7756*s**2 - 720 - 1200*s + 2853*s**3 + 5522*s**3 + r*s**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let l(h) be the second derivative of 440*h**7/21 - 395*h**6/12 - 139*h**5/10 + 237*h**4/4 - 45*h**3 - 4*h**2 - 68*h. Let m(s) be the first derivative of l(s). Suppose m(w) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "If -2175 - 114102*m + 340011*m**2 + 15783 + 36720*m**4 - 313266*m**3 - 20196*m**2 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let k(d) be the first derivative of 429*d**8/56 + 3491*d**7/280 - 301*d**6/30 - 1161*d**5/40 - 45*d**4/2 - 13*d**3/3 - 48. Let a(t) be the third derivative of k(t). If a(p) = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let n(c) be the second derivative of -7744*c**6/15 - 1056*c**5/5 + 5569*c**4/6 + 99*c**3 - 630*c**2 - 6674*c. Suppose n(m) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let 83775/17*a**2 + 11076*a**3 + 15786/17*a + 1080/17 + 8619*a**4 = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let z(f) be the third derivative of 55*f**10/2646 - 265*f**9/5292 + 47*f**8/2352 + 53*f**7/980 - 3*f**6/35 + 7*f**5/30 + 33*f**2. Let a(y) be the third derivative of z(y). Let a(x) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Let n(k) be the third derivative of 68*k**7/3 + 10343*k**6/120 - 689*k**5/5 + 129*k**4/8 + 63*k**3 + 177*k**2. Find the value of n + m, where n/m is the second largest root of n(v) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let g(j) be the first derivative of -43 - 243/8*j + 945/8*j**3 + 567/16*j**2 - 3519/32*j**4 - 231*j**5. Find the value of n + m, where n/m is the second largest root of g(t) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let d(x) be the first derivative of 3344*x**5 - 22479*x**4/4 + 441*x**3 + 1080*x**2 - 324*x + 1380. For the polynomial d(h), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let t(n) be the second derivative of 160*n**6/3 - 226*n**5/3 + 15*n**4 + 114*n**3/5 - 72*n**2/5 - 4*n + 3. Express the second largest root of t(i) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -217020/19*i**3 + 88296/19*i**2 + 15120/19 + 70200/19*i**4 + 98316/19*i = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Let 1080 - 5163*g**2 + 8334*g**4 + 75171*g**3 + 5631*g**4 + 882*g - 2520*g**2 - 78195*g**3 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Let b(y) be the third derivative of 0 - 6*y**3 + 242/45*y**6 - 2*y**4 - 18*y**2 - 2662/135*y**7 + 0*y + 66/5*y**5. Suppose b(a) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let p(x) = -112311*x**4 + 101119*x**3 - 3321*x**2 - 14463*x + 2601. Let k(a) = 56156*a**4 - 50560*a**3 + 1660*a**2 + 7232*a - 1300. Let d(t) = -7*k(t) - 4*p(t). Let j(r) = -18717*r**4 + 16852*r**3 - 555*r**2 - 2409*r + 435. Let h(v) = 3*d(v) + 8*j(v). Suppose h(u) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Let i(r) = -43125*r**4 - 34211*r**3 - 859*r**2 + 4531*r + 869. Let x(q) = 2266*q + 434 - 6455*q**4 - 15107*q**4 - 11434*q**3 - 5672*q**3 - 430*q**2. Let g(d) = -2*i(d) + 5*x(d). Let g(z) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of 58707*g**2 - 266712*g**3 - 14288*g**4 + 15384*g - 7128 - 44617*g**4 + 15774*g = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Express the second largest root of -2250*x**4 - 758 - 38*x**2 + 893 + 893*x**3 - 3018*x**3 + 657*x + 293*x**2 = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Suppose 1048959/23*q - 164160/23 - 24843/23*q**4 - 1359357/23*q**2 - 443079/23*q**3 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Let i(j) = 2 - 5*j. Let u be i(0). Find the value of n + m, where n/m is the second largest root of -28*p - 521*p - 108 + 3910*p**3 - 16*p**2 + 4400*p**4 + 163*p**u = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let n(w) be the first derivative of 700*w**5 - 850*w**4 - 5500*w**3/3 + 3564*w**2 - 2016*w + 1599. Express the second largest root of n(c) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let x(s) be the second derivative of 216*s**6/7 + 2277*s**5/10 + 247*s**4/4 - 3586*s**3/7 - 1035*s**2/2 + 179*s + 2. Let x(l) = 0. Find the second largest root in the form of n/m where n and m are coprime to each other. Return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Let q be (138/(-18))/23*-12. Suppose 4050/13*v**2 + 1215/13 + 18000/13*v**3 - 20625/13*v**q - 6480/13*v = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Suppose -1642 + 1571*p**2 - 5112*p + 51822*p**3 + 202 + 4607*p**2 + 3750*p**2 + 43472*p**4 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let n = 87743 + -87741. For the polynomial 375*f + 1041/11*f**n - 12558/11*f**3 - 11760/11*f**4 + 900/11, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let u(g) be the second derivative of 5481*g**6/5 + 7299*g**5/20 - 2111*g**4/3 - 327*g**3/2 + 90*g**2 - 5834*g. Express the second largest root of u(d) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Let s be (2 + -6)/(-5 + 148172/29636). Suppose -5863*x**3 + 263*x**3 - 4738*x**2 - s*x**3 + 226*x**2 + 432 + 1958*x**3 + 1332*x - 15400*x**4 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Let v(h) be the second derivative of 715*h**7/42 - 171*h**6/4 + 1591*h**5/60 + 15*h**4 - 24*h**3 - 26*h**2 - 33*h. Let l(b) be the first derivative of v(b). Suppose l(a) = 0. If the second largest root can be written as n/m where n and m are coprime, what is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Let c(z) be the third derivative of 2080*z**7/21 + 105*z**6 - 6*z**5/5 - 189*z**4/4 - 27*z**3 - 123*z**2. Express the second largest root of c(g) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Let a be (30/25)/((-180)/(-300)). If 3699/20*x - 2871/10*x**a - 192*x**3 - 567/20 + 480*x**4 = 0, what is n + m where n/m is the second largest root in simplified form?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the value of n + m, where n/m is the second largest root of -157216/9*q**2 - 640 + 563200/9*q**4 - 20768/3*q + 13760*q**3 = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Suppose -72 = 147*f + 140*f - 311*f. Let -27*m + 981*m**2 + 705/7*m**f - 324/7 - 3861*m**4 = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Let y(n) be the first derivative of 1664*n**5 + 1872*n**4 + 19 - 1053/5*n + 546/5*n**3 - 1053/2*n**2. For y(w) = 0, find the second largest root in simplified form n/m and return n + m.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}