messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"content": "Let i(o) be the first derivative of 2420*o**4/9 - 4070*o**3/9 - 610*o**2 - 210*o - 109. Suppose i(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"
}
] | 8 | MATH |
[
{
"content": "Let i(m) be the second derivative of 60/13*m**5 + 0 + 15/26*m**4 - 9/2*m**3 + 10*m - 81/26*m**2. Express the second largest root of i(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"
}
] | 7 | MATH |
[
{
"content": "Suppose 5*x - 3*j - 10 = 8, 0 = -2*x - 4*j + 2. For the polynomial -375*w**2 + 93 + 362*w - 1250*w**x + 42 + 88*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"
}
] | 7 | MATH |
[
{
"content": "Express the second largest root of 243/5*r - 4719/5*r**3 + 297*r**2 - 81/5 = 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"
}
] | 10 | MATH |
[
{
"content": "Find the value of n + m, where n/m is the second largest root of -326*a**2 - 221 - 51*a**3 + 581 - 43*a**3 - 536*a**3 + 816*a = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Let h(s) = 89*s - 1270. Let d be h(30). Express the second largest root of 260*i + 3980/9*i**2 - 80 - d*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"
}
] | 13 | MATH |
[
{
"content": "If 46354*i**2 - 2640*i**3 - 220 - 95 - 43004*i**2 - 45*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"
}
] | 11 | MATH |
[
{
"content": "Let y(q) be the second derivative of -81/20*q**2 - 27/40*q**3 + 33/8*q**5 + 135/16*q**4 - 24*q + 0. For the polynomial y(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": "us... | 7 | MATH |
[
{
"content": "Suppose 7*u = 16 - 2. Suppose 632*w - 14 - 92 - 2799*w**u + 3003*w**3 + 205*w + 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"
}
] | 14 | MATH |
[
{
"content": "Let l(m) be the third derivative of 131/35*m**5 - 4/3*m**6 - 30/7*m**4 - 10*m**2 + 0*m + 0 + 18/7*m**3. For the polynomial l(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":... | 10 | MATH |
[
{
"content": "Let o(n) be the first derivative of 81/8*n + 15/8*n**3 + 1 + 27*n**2 - 825/16*n**4. Let o(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"
}
] | 8 | MATH |
[
{
"content": "Let v = -244 - -2825/8. If 189/8 + 435/8*y**2 - 825/8*y**3 + 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"
}
] | 8 | MATH |
[
{
"content": "Let x(u) be the second derivative of -11*u**7/40 + 9*u**6/64 + 27*u**5/80 - 27*u**4/64 + 13*u**3/6 + 13*u. Let o(q) be the second derivative of x(q). Express the second largest root of o(c) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{You... | 14 | MATH |
[
{
"content": "Let l(w) = -156*w**3 + 2772*w**2 - 11988*w - 2884. Let h(c) = -52*c**3 + 924*c**2 - 3996*c - 962. Let r(t) = 16*h(t) - 5*l(t). 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": "... | 10 | MATH |
[
{
"content": "Let v(q) be the third derivative of -175*q**6/33 - 775*q**5/33 - 405*q**4/11 - 240*q**3/11 + 6*q**2 - 4*q. For the polynomial v(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}",
"rol... | 1 | MATH |
[
{
"content": "If -3025*j**3 + 52*j - 1176*j**2 + 10*j - 639*j**2 + 135 + 163*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"
}
] | 8 | MATH |
[
{
"content": "If 160*r**3 - 108/7 + 732/7*r**2 - 144/7*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"
}
] | 4 | MATH |
[
{
"content": "Let h(a) be the third derivative of 147*a**6/10 + 238*a**5/5 + 457*a**4/8 + 30*a**3 + 8*a**2 + 7. If h(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"
}
] | 3 | MATH |
[
{
"content": "Let f(p) be the third derivative of -16/5*p**5 + 0 + 0*p - 8/3*p**6 + 15/8*p**4 + 12*p**2 + 9/2*p**3. For the polynomial f(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": "... | 5 | MATH |
[
{
"content": "Let 3435*j**3 - 3685*j**2 + 2615*j**3 + 213*j + 138 + 177 - 813*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"
}
] | 14 | MATH |
[
{
"content": "Let g(q) = -198*q**3 - 67*q**2 + 142*q + 61. Let y(a) = -197*a**3 - 68*a**2 + 144*a + 60. Let k(j) = -3*g(j) + 2*y(j). Suppose k(t) = 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}",
"rol... | 2 | MATH |
[
{
"content": "Let o(g) be the third derivative of -2*g**7/13 + 449*g**6/780 - 45*g**5/52 + 9*g**4/13 - 5*g**3/2 - 9*g**2. Let x(c) be the first derivative of o(c). Express the second largest root of x(u) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex format: \\boxed{You... | 10 | MATH |
[
{
"content": "Let c(g) be the first derivative of -2475*g**4/4 - 1060*g**3/3 + 555*g**2/2 + 180*g + 89. Let c(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"
}
] | 8 | MATH |
[
{
"content": "Let n(i) be the first derivative of 540/7*i**2 - 375/2*i**4 - 825/7*i**3 + 7 + 405/7*i. For n(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"
}
] | 7 | MATH |
[
{
"content": "Let l(q) = 553*q - 2209. Let a be l(4). If 375/16*c**a - 135/16*c - 225/16*c**2 + 81/16 = 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"
}
] | 2 | MATH |
[
{
"content": "Let f(s) = -28600*s**3 + 8029*s**2 + 2580*s - 720. Let c(w) = 347*w**2 + 7150*w**3 - 645*w + 180 - 1773*w**2 - 581*w**2. Let r(x) = 9*c(x) + 2*f(x). Suppose r(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{Y... | 14 | MATH |
[
{
"content": "Let u(n) be the third derivative of 77*n**6/3 - 3679*n**5/15 + 643*n**4/2 - 168*n**3 - 73*n**2. If u(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"
}
] | 15 | MATH |
[
{
"content": "Let z(y) be the second derivative of -5*y**8/168 + y**7/21 + 5*y**6/128 - 9*y**5/64 - y**4/6 - 3*y. Let a(o) be the third derivative of z(o). If a(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"... | 11 | MATH |
[
{
"content": "Let m be (-46023)/(-138) - (3*-1 - 1). Suppose -2475/2*h**3 - 243/8 + 891/8*h + m*h**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"
}
] | 14 | MATH |
[
{
"content": "Let c(a) = -a**3 - 5*a**2 - 7*a - 64. Let z be c(-6). Suppose -14/3*m - z + 490/9*m**3 + 574/9*m**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"
}
] | 2 | MATH |
[
{
"content": "For 1800*c**3 - 190*c + 755 + 4875*c**2 - 3644*c + 564*c**3 - 2267 + 486*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"
}
] | 7 | MATH |
[
{
"content": "If -360/17 - 2310/17*d**3 + 432/17*d**2 + 1374/17*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"
}
] | 14 | MATH |
[
{
"content": "Let m(x) = 5797*x**3 + 8887*x**2 + 4440*x + 731. Let k(a) = 1933*a**3 + 2963*a**2 + 1480*a + 244. Let u(w) = 11*k(w) - 4*m(w). If u(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"
}
] | 3 | MATH |
[
{
"content": "Suppose 9*f - 37 = -10. If -2800/9*u**f - 320*u**2 - 12 - 108*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"
}
] | 4 | MATH |
[
{
"content": "Let n(y) be the second derivative of 261*y**5/4 - 13*y**4/2 - 12*y**3 - 107*y - 1. If n(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"
}
] | 1 | MATH |
[
{
"content": "Let j(w) = 3025*w**3 + 1817*w**2 - 223*w - 137. Let u(s) = -s**3 + 7*s**2 - 8*s + 7. Let p be u(6). Let d(h) = -6050*h**3 - 3635*h**2 + 445*h + 275. Let b(m) = p*j(m) - 2*d(m). 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... | 8 | MATH |
[
{
"content": "Suppose -45 + 1197/4*n**3 + 1101/4*n - 4119/8*n**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"
}
] | 11 | MATH |
[
{
"content": "Let m(g) = 4*g**2 - 10*g + 6. Let u be m(7). If -u + 545*p**3 - 3625*p**3 - 96*p - 48 + 531*p + 1285*p**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"
}
] | 15 | MATH |
[
{
"content": "Let -3328/3*s**3 + 195/2 - 2080/3*s**2 + 156*s = 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"
}
] | 5 | MATH |
[
{
"content": "Let o(d) be the third derivative of 32*d**6/3 - 48*d**5/5 - 69*d**4/2 - 27*d**3 - 54*d**2. 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"
}
] | 7 | MATH |
[
{
"content": "If -989*o**2 - 15699*o**3 + 15559*o**3 + 1003*o**4 + 9397*o**4 - 10144*o**2 - 2682*o + 648 = 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"
}
] | 23 | MATH |
[
{
"content": "Express the second largest root of -5020*v**3 + 448*v**2 - 84*v**2 + 3798*v + 338*v**2 + 229 - 7920*v**4 + 581 - 5698*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"
}
] | 8 | MATH |
[
{
"content": "Let h = 21586 + -12322. Express the second largest root of 19 - h*m**4 + 15368*m**3 - 28176*m**4 - 733 - 294 + 14260*m**2 - 1476*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"
}
] | 17 | MATH |
[
{
"content": "Let v(i) be the first derivative of -1815*i**7/91 + 5203*i**6/312 + 1117*i**5/52 - 645*i**4/104 - 315*i**3/26 + 4*i**2 - 5*i + 98. Let r(n) be the second derivative of v(n). Find the value of n + m, where n/m is the second largest root of r(t) = 0 in its simplest form.\n\nPresent the answer in LaT... | 14 | MATH |
[
{
"content": "Suppose 4160*a**3 + 4480*a**4 - 585*a - 12090/7*a**2 + 1080/7 = 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"
}
] | 17 | MATH |
[
{
"content": "Let g(q) be the third derivative of -125*q**7/36 + 575*q**6/24 + 225*q**5/8 - 555*q**4/4 - 315*q**3 + 3*q**2 + 1041. Let g(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}",
... | 11 | MATH |
[
{
"content": "Suppose 2*s = -16, 3*t - 389*s + 28 = -394*s. For the polynomial 17325/19*p**3 - 3699/19*p**2 + 18150/19*p**t + 729/19 - 3321/19*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}",
"rol... | 2 | MATH |
[
{
"content": "Let w(a) be the first derivative of -500*a**6 + 625*a**5 + 675*a**4/2 - 855*a**3/2 - 675*a**2/2 - 19*a - 1. Let b(z) be the first derivative of w(z). For the polynomial b(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 La... | 8 | MATH |
[
{
"content": "Let p(a) be the third derivative of 112/27*a**6 - 140/9*a**3 + 2191/540*a**5 + 0 + 5/6*a**7 - 679/108*a**4 - 2*a - 8*a**2. Suppose p(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}",
... | 2 | MATH |
[
{
"content": "Let n(h) be the third derivative of 35*h**9/54 - 99*h**8/64 - 4*h**7/7 + 81*h**6/16 - 27*h**5/4 + 13*h**4/12 - h**3/3 - 4*h**2 - 11. Let m(d) be the second derivative of n(d). Let m(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\nPr... | 10 | MATH |
[
{
"content": "Let 44496/13*t - 1004400/13*t**3 - 12780*t**2 + 10368/13 - 1134000/13*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"
}
] | 11 | MATH |
[
{
"content": "Let h(j) = -8097*j**4 - 43067*j**3 + 6895*j**2 + 12771*j - 3074. Let q(u) = 24288*u**4 + 129202*u**3 - 20687*u**2 - 38313*u + 9223. Let t(r) = -11*h(r) - 4*q(r). For t(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 ... | 14 | MATH |
[
{
"content": "For the polynomial -402 + 158 + 414 - 4157*c**2 + 15288*c**4 - 15862*c**3 + 310 + 2228*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"
}
] | 17 | MATH |
[
{
"content": "Let l(r) be the third derivative of 429*r**7/10 - 47*r**6/24 - 763*r**5/20 + 21*r**4/8 + 18*r**3 + 4*r**2 + 6. Express the second largest root of l(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"
}
] | 14 | MATH |
[
{
"content": "Let q(g) be the first derivative of -400*g**6 - 135*g**5 + 315*g**4 + 81*g**3/2 - 243*g**2/2 - 21*g + 15. Let y(p) be the first derivative of q(p). Suppose y(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{Yo... | 13 | MATH |
[
{
"content": "Let n(t) be the second derivative of 5*t**9/98 + 1159*t**8/3136 + 241*t**7/245 + 771*t**6/560 + 81*t**5/70 + 143*t**4/12 + 14*t. Let p(i) be the third derivative of n(i). Let p(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... | 5 | MATH |
[
{
"content": "Let w(p) be the second derivative of 637*p**6 + 7154*p**5/5 - 3239*p**4/6 - 3680*p**3/3 - 528*p**2 + 7*p. For w(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"
}
] | 10 | MATH |
[
{
"content": "Let v(h) = 77442 - 968*h. Let s be v(80). If -93600/7*b**4 - 23355/7*b - 13680*b**s - 2025/7 - 162780/7*b**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"
}
] | 7 | MATH |
[
{
"content": "Let h(m) be the third derivative of -8*m**9/27 - 17*m**8/35 + 3*m**7/140 + 51*m**6/80 + 27*m**5/40 - 7*m**4/8 + 93*m**2. Let c(w) be the second derivative of h(w). Express the second largest root of c(s) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaTex forma... | 7 | MATH |
[
{
"content": "If 33696*m**3 + 2021*m**2 + 3150 - 12675*m + 498*m**2 - 24192*m**4 - 353*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"
}
] | 31 | MATH |
[
{
"content": "Let b(l) be the third derivative of -250/3*l**7 + 0*l + 965/12*l**5 + 225/2*l**6 - 20*l**2 - 110*l**4 + 0 - 120*l**3. 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}... | 11 | MATH |
[
{
"content": "For 4482/11*x - 45525/11*x**3 - 33489/11*x**2 + 3240/11 - 13650/11*x**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"
}
] | 7 | MATH |
[
{
"content": "Let l(o) = -14101*o**4 + 1721*o**3 + 4932*o**2 - 317. Let u(b) = 70508*b**4 - 8604*b**3 - 24660*b**2 + 1584. Let r(i) = 36*l(i) + 7*u(i). If r(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": "u... | 14 | MATH |
[
{
"content": "Let s(q) = -25153*q**4 - 28974*q**3 - 4878*q**2 + 2214*q + 481. Let o(a) = -25156*a**4 - 28974*a**3 - 4878*a**2 + 2214*a + 482. Let h(j) = -5*o(j) + 4*s(j). Let h(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... | 10 | MATH |
[
{
"content": "Let y(a) be the first derivative of 176*a**7/3 + 1711*a**6/30 - 957*a**5/10 - 171*a**4/4 + 90*a**3 - 3*a**2/2 - 15*a + 64. Let r(s) be the second derivative of y(s). Find the value of n + m, where n/m is the second largest root of r(u) = 0 in its simplest form.\n\nPresent the answer in LaTex forma... | 13 | MATH |
[
{
"content": "Let x(w) be the first derivative of 3234*w**5/5 + 24969*w**4/20 - 25432*w**3/5 + 9441*w**2/2 - 1620*w - 5261. Let x(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... | 13 | MATH |
[
{
"content": "Let 729/7 - 1785*d**4 - 1674/7*d**2 + 3528*d**3 - 648*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"
}
] | 10 | MATH |
[
{
"content": "Let q(n) be the third derivative of 11583*n**7/98 + 22311*n**6/20 - 474669*n**5/140 - 55809*n**4/14 + 11664*n**3 - 5620*n**2. Find the value of n + m, where n/m is the second largest root of q(a) = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 13 | MATH |
[
{
"content": "Let s(u) = 89100*u**4 + 236850*u**3 + 181985*u**2 + 26970*u - 8925. Let l(a) = -a**3 - a**2 + 7*a - 5. Let o(d) = 15*l(d) + s(d). For o(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"
}... | 4 | MATH |
[
{
"content": "For the polynomial 321*c - 318*c - 1326*c + 1200 + 3425*c**3 - 5273*c**2 + 3800*c**4 + 433*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"
}
] | 8 | MATH |
[
{
"content": "Let m(t) be the second derivative of -8151*t**6/2 + 18429*t**5/20 + 4095*t**4/4 - 351*t**3/2 - 162*t**2 + 139*t - 4. 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}"... | 19 | MATH |
[
{
"content": "For the polynomial -8093*u**2 + 33600*u**4 - 928 + 53640*u**3 + 366*u - 33*u + 172 + 30671*u**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"
}
] | 7 | MATH |
[
{
"content": "Let q(k) be the first derivative of -560*k**6/3 + 339*k**5 + 363*k**4/2 - 288*k**3 - 243*k**2 - 6*k - 55. Let l(f) be the first derivative of q(f). Let l(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 fo... | 8 | MATH |
[
{
"content": "Let n(o) be the second derivative of -380*o**6/3 + 2433*o**5/13 + 1467*o**4/13 - 792*o**3/13 - 648*o**2/13 + 29*o + 30. Suppose n(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}",
"ro... | 25 | MATH |
[
{
"content": "Let -10962/13*y + 17424/13*y**4 + 698895/13 + 147378/13*y**3 - 9397551/13*y**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"
}
] | 14 | MATH |
[
{
"content": "Let u be ((-876)/18)/(6/(-7731)) + 2. Express the second largest root of 8100 + u*k**2 - 18223*k + 5747*k - 33784*k + 312*k**3 - 27885*k**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"
}
] | 14 | MATH |
[
{
"content": "Let w(i) = -3297*i**4 + 16677*i**3 - 26427*i**2 + 16698*i - 3651. Let a(m) = -1648*m**4 + 8339*m**3 - 13214*m**2 + 8349*m - 1826. Let s(o) = 21*a(o) - 10*w(o). Let s(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... | 2 | MATH |
[
{
"content": "Let c = -323297 - -326771. Find the value of n + m, where n/m is the second largest root of 81 + c*z**2 + 4032*z**4 + 30648/5*z**3 + 4347/5*z = 0 in its simplest form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Let 243/5 - 2601/10*o**3 - 891/10*o - 13689/10*o**2 + 8547/2*o**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"
}
] | 43 | MATH |
[
{
"content": "Let c(h) be the first derivative of -1836*h**5 - 10749*h**4/2 + 52750*h**3/3 - 502*h**2 - 7728*h + 4029. Let c(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": "u... | 13 | MATH |
[
{
"content": "Let v(f) be the third derivative of 142*f + 3146/175*f**7 + 36/5*f**4 + 0 + 194/25*f**5 + f**2 - 1232/45*f**6 - 6*f**3. For the polynomial v(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 answe... | 14 | MATH |
[
{
"content": "Let r(q) = 323*q**2 - 6*q - 5. Let a be r(-5). For the polynomial -2058*y + 143 + 1888*y**2 - a*y**4 - 801*y**3 + 2951*y**3 + 217 + 3520*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}... | 13 | MATH |
[
{
"content": "Let i(u) be the third derivative of -55*u**9/432 - 9*u**8/14 - 9*u**7/20 + 6*u**6/5 + 81*u**5/40 + 2*u**4/3 + u**3/2 + 32*u**2 - 2*u. Let p(z) be the second derivative of i(z). Let p(r) = 0. Calculate the second largest root as n/m where n and m are coprime integers. What is n + m?\n\nPresent the ... | 8 | MATH |
[
{
"content": "Let z(o) = 334388*o**4 + 118908*o**3 - 34008*o**2 - 17256*o - 1620. Let a(i) = -133755*i**4 - 47563*i**3 + 13603*i**2 + 6902*i + 648. Let h(d) = 12*a(d) + 5*z(d). For h(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... | 16 | MATH |
[
{
"content": "Let x(v) = 7023*v**4 + 45345*v**3 + 22340*v**2 - 33933*v - 11031. Let i(a) = a**4 + 3*a**3 - 3*a**2 + a - 2. Let w(j) = 3*i(j) - x(j). 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}",
... | 7 | MATH |
[
{
"content": "If -73332/11*h**3 - 45080/11*h**4 - 32724/11*h**2 - 1836/11*h + 972/11 = 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"
}
] | 4 | MATH |
[
{
"content": "If -48621101*v**2 - 54340*v**4 + 174598*v**3 + 48535291*v**2 + 7056 - 24805*v + 5401*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"
}
] | 33 | MATH |
[
{
"content": "Let v be 26 - (8 + (5 - -9)). Suppose -3591/17*p**2 + 13200/17*p**v + 270*p**3 - 1944/17*p - 243/17 = 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"
}
] | 8 | MATH |
[
{
"content": "Let l(c) be the second derivative of 44*c**9/1071 + 61*c**8/2380 - 121*c**7/840 - 81*c**6/1360 + 9*c**5/34 + 5*c**4/4 + 27*c. Let x(i) be the third derivative of l(i). Let x(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... | 14 | MATH |
[
{
"content": "Let i(m) be the third derivative of -2704*m**7/161 - 7709*m**6/230 - 217*m**5/46 + 534*m**4/23 + 432*m**3/23 + 2*m**2 - m - 1234. Suppose i(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}... | 9 | MATH |
[
{
"content": "Let h(l) be the third derivative of -715*l**9/756 + 151*l**8/56 - 751*l**7/630 - 18*l**6/5 + 24*l**5/5 - 23*l**4/4 - 3*l**2 - l. Let d(k) be the second derivative of h(k). Express the second largest root of d(u) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaT... | 8 | MATH |
[
{
"content": "Let j(l) be the second derivative of 1331*l**9/945 - 5687*l**8/3360 - 121*l**7/210 + 89*l**6/40 - 9*l**5/5 - 3*l**4/4 + 16*l + 2. Let n(c) be the third derivative of j(c). Express the second largest root of n(a) = 0 as n/m where n and m are coprime and calculate n + m.\n\nPresent the answer in LaT... | 14 | MATH |
[
{
"content": "Let s(n) be the first derivative of -47 + 28160/13*n**5 + 4320/13*n - 640*n**4 - 16840/13*n**3 + 180*n**2. For s(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"
}
] | 11 | MATH |
[
{
"content": "Let t(g) be the first derivative of -1144*g**5 + 14093*g**4/9 + 237764*g**3/27 - 24340*g**2 + 21600*g + 1307. For the polynomial t(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}",
"... | 19 | MATH |
[
{
"content": "Let h(a) be the third derivative of -338/3*a**7 + 5*a**2 - 387/4*a**4 + 0 - 4693/20*a**6 - 4*a - 2043/10*a**5 - 27*a**3. If h(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"
}
] | 7 | MATH |
[
{
"content": "Let u be (1290/(-104))/(230910/(-3784) + 61). For the polynomial -837/13*q + 18150/13*q**4 - 4572/13*q**2 + 324/13 + u*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": "us... | 14 | MATH |
[
{
"content": "For the polynomial 1632*r**4 + 33872/21*r**2 - 228/7*r - 528/7 - 68276/21*r**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"
}
] | 11 | MATH |
[
{
"content": "Let p(b) be the second derivative of 572/15*b**6 + 0 + 14287/100*b**5 - 741/10*b**3 - 351/5*b**2 + 793/10*b**4 - 166*b. Express the second largest root of p(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"... | 8 | MATH |
[
{
"content": "Let v be 14/(756/12069) + -3. Suppose -735*s**4 - 243/10 + 81/2*s - v*s**3 + 2673/10*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"
}
] | 13 | MATH |
[
{
"content": "Let a(m) = 155034*m**4 + 60732*m**3 - 28929*m**2 - 6390*m + 1626. Let n(w) = -310069*w**4 - 121465*w**3 + 57859*w**2 + 12777*w - 3251. Let u(d) = 11*a(d) + 6*n(d). Let u(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 an... | 19 | MATH |
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