question
stringlengths 780
847
| answer
stringlengths 3
41
| metadata
dict | difficulty
int64 2
5
|
|---|---|---|---|
Find the real value(s) of w in the equation: -2*w = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-2*w",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 0,
"variable": "w"
}
| 2
|
Solve the polynomial equation for real b:
6*b**2 - 2*b = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0, 0.3333
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "6*b**2 - 2*b",
"real_solutions": [
0,
0.3333
],
"source_dataset": "polynomial_equations",
"source_index": 1,
"variable": "b"
}
| 2
|
Find the real value(s) of p in the equation: -8*p = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-8*p",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 2,
"variable": "p"
}
| 2
|
Solve the polynomial equation for real d:
-5*d**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-5*d**2",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 3,
"variable": "d"
}
| 2
|
Solve for real c: 14*c**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "14*c**2",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 4,
"variable": "c"
}
| 2
|
Find the real value(s) of n in the equation: 19*n = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "19*n",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 5,
"variable": "n"
}
| 2
|
Solve the polynomial equation for real t:
-18*t**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-18*t**2",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 6,
"variable": "t"
}
| 2
|
Solve for real z: -11*z = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-11*z",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 7,
"variable": "z"
}
| 2
|
Find the real value(s) of r in the equation: 2*r**2 - 6 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.7321, 1.7321
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "2*r**2 - 6",
"real_solutions": [
-1.7321,
1.7321
],
"source_dataset": "polynomial_equations",
"source_index": 8,
"variable": "r"
}
| 2
|
Solve the polynomial equation for real h:
7 - 9*h = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.7778
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "7 - 9*h",
"real_solutions": [
0.7778
],
"source_dataset": "polynomial_equations",
"source_index": 9,
"variable": "h"
}
| 2
|
Determine the real value(s) of k that satisfies: 11*k = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "11*k",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 10,
"variable": "k"
}
| 2
|
Determine the real value(s) of v that satisfies: 15*v = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "15*v",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 11,
"variable": "v"
}
| 2
|
Solve for real e: -7*e**2 + 13*e = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0, 1.8571
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "-7*e**2 + 13*e",
"real_solutions": [
0,
1.8571
],
"source_dataset": "polynomial_equations",
"source_index": 12,
"variable": "e"
}
| 2
|
Solve the polynomial equation for real c:
-3*c = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-3*c",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 13,
"variable": "c"
}
| 2
|
Solve for real t: -9*t = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "-9*t",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 14,
"variable": "t"
}
| 2
|
Solve the polynomial equation for real p:
-7*p**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-7*p**2",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 15,
"variable": "p"
}
| 2
|
Determine the real value(s) of u that satisfies: -u - 7 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-7.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-u - 7",
"real_solutions": [
-7
],
"source_dataset": "polynomial_equations",
"source_index": 16,
"variable": "u"
}
| 2
|
Determine the real value(s) of h that satisfies: 5*h - 18 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
3.6
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "5*h - 18",
"real_solutions": [
3.6
],
"source_dataset": "polynomial_equations",
"source_index": 17,
"variable": "h"
}
| 2
|
Find the real value(s) of l in the equation: 4*l**2 + 8*l = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-2.0, 0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "4*l**2 + 8*l",
"real_solutions": [
-2,
0
],
"source_dataset": "polynomial_equations",
"source_index": 18,
"variable": "l"
}
| 2
|
Determine the real value(s) of r that satisfies: -6*r = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-6*r",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 19,
"variable": "r"
}
| 2
|
Solve for real u: -8*u - 6 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-0.75
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-8*u - 6",
"real_solutions": [
-0.75
],
"source_dataset": "polynomial_equations",
"source_index": 20,
"variable": "u"
}
| 2
|
Determine the real value(s) of q that satisfies: -2*q**2 - 6*q = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-3.0, 0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "-2*q**2 - 6*q",
"real_solutions": [
-3,
0
],
"source_dataset": "polynomial_equations",
"source_index": 21,
"variable": "q"
}
| 2
|
Solve the polynomial equation for real r:
5*r + 1 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-0.2
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "5*r + 1",
"real_solutions": [
-0.2
],
"source_dataset": "polynomial_equations",
"source_index": 22,
"variable": "r"
}
| 2
|
Find the real value(s) of p in the equation: 3*p = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "3*p",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 23,
"variable": "p"
}
| 2
|
Find the real value(s) of s in the equation: 5*s = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "5*s",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 24,
"variable": "s"
}
| 2
|
Solve for real c: 3*c = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "3*c",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 25,
"variable": "c"
}
| 2
|
Determine the real value(s) of z that satisfies: -18*z**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-18*z**2",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 26,
"variable": "z"
}
| 2
|
Solve the polynomial equation for real x:
2*x + 6 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-3.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "2*x + 6",
"real_solutions": [
-3
],
"source_dataset": "polynomial_equations",
"source_index": 27,
"variable": "x"
}
| 2
|
Solve the polynomial equation for real d:
6*d**2 + 3*d - 10 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.565, 1.065
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "6*d**2 + 3*d - 10",
"real_solutions": [
-1.565,
1.065
],
"source_dataset": "polynomial_equations",
"source_index": 28,
"variable": "d"
}
| 2
|
Determine the real value(s) of m that satisfies: -5*m - 5 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "-5*m - 5",
"real_solutions": [
-1
],
"source_dataset": "polynomial_equations",
"source_index": 29,
"variable": "m"
}
| 2
|
Solve for real c: -13*c = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "-13*c",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 30,
"variable": "c"
}
| 2
|
Find the real value(s) of k in the equation: -4*k - 8 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-2.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "-4*k - 8",
"real_solutions": [
-2
],
"source_dataset": "polynomial_equations",
"source_index": 31,
"variable": "k"
}
| 2
|
Determine the real value(s) of v that satisfies: 11*v - 4 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.3636
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "11*v - 4",
"real_solutions": [
0.3636
],
"source_dataset": "polynomial_equations",
"source_index": 32,
"variable": "v"
}
| 2
|
Solve the polynomial equation for real y:
-5*y**2 + 6*y = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0, 1.2
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-5*y**2 + 6*y",
"real_solutions": [
0,
1.2
],
"source_dataset": "polynomial_equations",
"source_index": 33,
"variable": "y"
}
| 2
|
Find the real value(s) of n in the equation: -n**2 - 8*n - 4 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-7.4641, -0.5359
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "-n**2 - 8*n - 4",
"real_solutions": [
-7.4641,
-0.5359
],
"source_dataset": "polynomial_equations",
"source_index": 34,
"variable": "n"
}
| 2
|
Solve for real k: 4*k**2 - 2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-0.7071, 0.7071
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "4*k**2 - 2",
"real_solutions": [
-0.7071,
0.7071
],
"source_dataset": "polynomial_equations",
"source_index": 35,
"variable": "k"
}
| 2
|
Solve the polynomial equation for real g:
12*g = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "12*g",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 36,
"variable": "g"
}
| 2
|
Find the real value(s) of k in the equation: 14*k**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "14*k**2",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 37,
"variable": "k"
}
| 2
|
Find the real value(s) of k in the equation: -9*k**2 + 8*k = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0, 0.8889
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "-9*k**2 + 8*k",
"real_solutions": [
0,
0.8889
],
"source_dataset": "polynomial_equations",
"source_index": 38,
"variable": "k"
}
| 2
|
Determine the real value(s) of v that satisfies: 3*v = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "3*v",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 39,
"variable": "v"
}
| 2
|
Solve for real e: 9 - 5*e**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.3416, 1.3416
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "9 - 5*e**2",
"real_solutions": [
-1.3416,
1.3416
],
"source_dataset": "polynomial_equations",
"source_index": 40,
"variable": "e"
}
| 2
|
Solve the polynomial equation for real l:
6*l = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "6*l",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 41,
"variable": "l"
}
| 2
|
Solve the polynomial equation for real z:
z**2 + 6*z = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-6.0, 0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "z**2 + 6*z",
"real_solutions": [
-6,
0
],
"source_dataset": "polynomial_equations",
"source_index": 42,
"variable": "z"
}
| 2
|
Solve for real g: 8*g + 13 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.625
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "8*g + 13",
"real_solutions": [
-1.625
],
"source_dataset": "polynomial_equations",
"source_index": 43,
"variable": "g"
}
| 2
|
Find the real value(s) of o in the equation: -12*o = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-12*o",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 44,
"variable": "o"
}
| 2
|
Find the real value(s) of e in the equation: 12*e = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "12*e",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 45,
"variable": "e"
}
| 2
|
Find the real value(s) of o in the equation: 9*o - 7 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.7778
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "9*o - 7",
"real_solutions": [
0.7778
],
"source_dataset": "polynomial_equations",
"source_index": 46,
"variable": "o"
}
| 2
|
Solve for real c: -2*c**2 - 7*c = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-3.5, 0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-2*c**2 - 7*c",
"real_solutions": [
-3.5,
0
],
"source_dataset": "polynomial_equations",
"source_index": 47,
"variable": "c"
}
| 2
|
Solve for real g: -2*g = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "-2*g",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 48,
"variable": "g"
}
| 2
|
Find the real value(s) of k in the equation: -12*k = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-12*k",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 49,
"variable": "k"
}
| 2
|
Determine the real value(s) of p that satisfies: -7*p**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-7*p**2",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 50,
"variable": "p"
}
| 2
|
Solve for real f: 9*f = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "9*f",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 51,
"variable": "f"
}
| 2
|
Determine the real value(s) of t that satisfies: -4*t = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-4*t",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 52,
"variable": "t"
}
| 2
|
Solve for real t: t + 6 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-6.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "t + 6",
"real_solutions": [
-6
],
"source_dataset": "polynomial_equations",
"source_index": 53,
"variable": "t"
}
| 2
|
Determine the real value(s) of n that satisfies: 6*n**2 - 7 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.0801, 1.0801
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "6*n**2 - 7",
"real_solutions": [
-1.0801,
1.0801
],
"source_dataset": "polynomial_equations",
"source_index": 54,
"variable": "n"
}
| 2
|
Solve for real c: 7 - 11*c**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-0.7977, 0.7977
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "7 - 11*c**2",
"real_solutions": [
-0.7977,
0.7977
],
"source_dataset": "polynomial_equations",
"source_index": 55,
"variable": "c"
}
| 2
|
Solve the polynomial equation for real n:
8 - 17*n = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.4706
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "8 - 17*n",
"real_solutions": [
0.4706
],
"source_dataset": "polynomial_equations",
"source_index": 56,
"variable": "n"
}
| 2
|
Determine the real value(s) of k that satisfies: 2*k**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "2*k**2",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 57,
"variable": "k"
}
| 2
|
Find the real value(s) of e in the equation: -3*e = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "-3*e",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 58,
"variable": "e"
}
| 2
|
Solve for real u: 8 - 5*u = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
1.6
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "8 - 5*u",
"real_solutions": [
1.6
],
"source_dataset": "polynomial_equations",
"source_index": 59,
"variable": "u"
}
| 2
|
Find the real value(s) of e in the equation: -5*e**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-5*e**2",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 60,
"variable": "e"
}
| 2
|
Solve the polynomial equation for real y:
4*y**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "4*y**2",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 61,
"variable": "y"
}
| 2
|
Find the real value(s) of a in the equation: -3*a = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "-3*a",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 62,
"variable": "a"
}
| 2
|
Solve for real u: 5*u**2 - 10 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.4142, 1.4142
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "5*u**2 - 10",
"real_solutions": [
-1.4142,
1.4142
],
"source_dataset": "polynomial_equations",
"source_index": 63,
"variable": "u"
}
| 2
|
Determine the real value(s) of y that satisfies: 10*y**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 2,
"polynomial_expr": "10*y**2",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 64,
"variable": "y"
}
| 2
|
Determine the real value(s) of h that satisfies: 7*h**2 - 2*h - 10 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.0609, 1.3466
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "7*h**2 - 2*h - 10",
"real_solutions": [
-1.0609,
1.3466
],
"source_dataset": "polynomial_equations",
"source_index": 65,
"variable": "h"
}
| 2
|
Determine the real value(s) of e that satisfies: 3*e = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "3*e",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 66,
"variable": "e"
}
| 2
|
Find the real value(s) of k in the equation: 6*k + 10 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.6667
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "6*k + 10",
"real_solutions": [
-1.6667
],
"source_dataset": "polynomial_equations",
"source_index": 67,
"variable": "k"
}
| 2
|
Find the real value(s) of o in the equation: 6*o = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 1,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "6*o",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 68,
"variable": "o"
}
| 2
|
Solve for real f: -6*f**2 - 6*f = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.0, 0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
1,
2
],
"terms": [
2,
3
]
},
"num_terms": 3,
"polynomial_expr": "-6*f**2 - 6*f",
"real_solutions": [
-1,
0
],
"source_dataset": "polynomial_equations",
"source_index": 69,
"variable": "f"
}
| 2
|
Solve the polynomial equation for real w:
-4*w**2 - 18*w = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-4.5, 0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 3,
"polynomial_expr": "-4*w**2 - 18*w",
"real_solutions": [
-4.5,
0
],
"source_dataset": "polynomial_equations",
"source_index": 0,
"variable": "w"
}
| 3
|
Determine the real value(s) of b that satisfies: 12*b**3 - 17*b**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0, 1.4167
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 3,
"polynomial_expr": "12*b**3 - 17*b**2",
"real_solutions": [
0,
1.4167
],
"source_dataset": "polynomial_equations",
"source_index": 1,
"variable": "b"
}
| 3
|
Determine the real value(s) of s that satisfies: 7*s**3 - 15*s**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0, 2.1429
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "7*s**3 - 15*s**2",
"real_solutions": [
0,
2.1429
],
"source_dataset": "polynomial_equations",
"source_index": 2,
"variable": "s"
}
| 3
|
Find the real value(s) of k in the equation: -11*k**3 - 6*k**2 + 10 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.8169
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "-11*k**3 - 6*k**2 + 10",
"real_solutions": [
0.8169
],
"source_dataset": "polynomial_equations",
"source_index": 3,
"variable": "k"
}
| 3
|
Find the real value(s) of c in the equation: 19*c**3 + 9*c = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 3,
"polynomial_expr": "19*c**3 + 9*c",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 4,
"variable": "c"
}
| 3
|
Find the real value(s) of n in the equation: -23*n**2 + 2*n = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0, 0.087
|
{
"degree": 2,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "-23*n**2 + 2*n",
"real_solutions": [
0,
0.087
],
"source_dataset": "polynomial_equations",
"source_index": 5,
"variable": "n"
}
| 3
|
Solve for real t: -14*t**3 - 4*t**2 - 8*t = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 3,
"polynomial_expr": "-14*t**3 - 4*t**2 - 8*t",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 6,
"variable": "t"
}
| 3
|
Determine the real value(s) of c that satisfies: 2*c**3 + 2*c**2 - 26 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
2.0609
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "2*c**3 + 2*c**2 - 26",
"real_solutions": [
2.0609
],
"source_dataset": "polynomial_equations",
"source_index": 7,
"variable": "c"
}
| 3
|
Determine the real value(s) of r that satisfies: 6*r**3 + 12*r**2 + 8*r = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "6*r**3 + 12*r**2 + 8*r",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 8,
"variable": "r"
}
| 3
|
Determine the real value(s) of t that satisfies: -4*t**3 - 2*t**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-0.5, 0.0
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "-4*t**3 - 2*t**2",
"real_solutions": [
-0.5,
0
],
"source_dataset": "polynomial_equations",
"source_index": 9,
"variable": "t"
}
| 3
|
Solve the polynomial equation for real o:
-6*o**3 + 8*o + 16 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
1.7028
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 3,
"polynomial_expr": "-6*o**3 + 8*o + 16",
"real_solutions": [
1.7028
],
"source_dataset": "polynomial_equations",
"source_index": 10,
"variable": "o"
}
| 3
|
Determine the real value(s) of v that satisfies: 12*v = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "12*v",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 11,
"variable": "v"
}
| 3
|
Solve the polynomial equation for real e:
16*e**3 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "16*e**3",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 12,
"variable": "e"
}
| 3
|
Solve the polynomial equation for real c:
-7*c**2 + 16*c = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0, 2.2857
|
{
"degree": 2,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 3,
"polynomial_expr": "-7*c**2 + 16*c",
"real_solutions": [
0,
2.2857
],
"source_dataset": "polynomial_equations",
"source_index": 13,
"variable": "c"
}
| 3
|
Determine the real value(s) of t that satisfies: 28*t**2 - 3*t = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0, 0.1071
|
{
"degree": 2,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "28*t**2 - 3*t",
"real_solutions": [
0,
0.1071
],
"source_dataset": "polynomial_equations",
"source_index": 14,
"variable": "t"
}
| 3
|
Solve for real b: -16*b**3 - 13*b**2 + 14*b = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.4261, 0.0, 0.6136
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 3,
"polynomial_expr": "-16*b**3 - 13*b**2 + 14*b",
"real_solutions": [
-1.4261,
0,
0.6136
],
"source_dataset": "polynomial_equations",
"source_index": 15,
"variable": "b"
}
| 3
|
Determine the real value(s) of u that satisfies: -12*u**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 3,
"polynomial_expr": "-12*u**2",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 16,
"variable": "u"
}
| 3
|
Solve for real h: h**2 - 18*h - 15 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-0.798, 18.798
|
{
"degree": 2,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "h**2 - 18*h - 15",
"real_solutions": [
-0.798,
18.798
],
"source_dataset": "polynomial_equations",
"source_index": 17,
"variable": "h"
}
| 3
|
Find the real value(s) of l in the equation: -16*l**3 + 11*l**2 + 2*l = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-0.1494, 0.0, 0.8369
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 3,
"polynomial_expr": "-16*l**3 + 11*l**2 + 2*l",
"real_solutions": [
-0.1494,
0,
0.8369
],
"source_dataset": "polynomial_equations",
"source_index": 18,
"variable": "l"
}
| 3
|
Solve the polynomial equation for real r:
11*r**2 - 13*r = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0, 1.1818
|
{
"degree": 2,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 3,
"polynomial_expr": "11*r**2 - 13*r",
"real_solutions": [
0,
1.1818
],
"source_dataset": "polynomial_equations",
"source_index": 19,
"variable": "r"
}
| 3
|
Determine the real value(s) of u that satisfies: 10*u**2 - 6*u - 12 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-0.8358, 1.4358
|
{
"degree": 2,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 3,
"polynomial_expr": "10*u**2 - 6*u - 12",
"real_solutions": [
-0.8358,
1.4358
],
"source_dataset": "polynomial_equations",
"source_index": 20,
"variable": "u"
}
| 3
|
Find the real value(s) of q in the equation: 3*q**3 + 3*q**2 + 10 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.9119
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "3*q**3 + 3*q**2 + 10",
"real_solutions": [
-1.9119
],
"source_dataset": "polynomial_equations",
"source_index": 21,
"variable": "q"
}
| 3
|
Find the real value(s) of r in the equation: 9*r**2 - 14 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.2472, 1.2472
|
{
"degree": 2,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "9*r**2 - 14",
"real_solutions": [
-1.2472,
1.2472
],
"source_dataset": "polynomial_equations",
"source_index": 22,
"variable": "r"
}
| 3
|
Solve the polynomial equation for real p:
11*p = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "11*p",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 23,
"variable": "p"
}
| 3
|
Find the real value(s) of c in the equation: -7*c**3 - 17*c**2 - 18*c = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "-7*c**3 - 17*c**2 - 18*c",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 24,
"variable": "c"
}
| 3
|
Solve for real c: -20*c**2 - 19*c = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-0.95, 0.0
|
{
"degree": 2,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "-20*c**2 - 19*c",
"real_solutions": [
-0.95,
0
],
"source_dataset": "polynomial_equations",
"source_index": 25,
"variable": "c"
}
| 3
|
Find the real value(s) of z in the equation: -34*z**3 - 11*z = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
0.0
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 3,
"polynomial_expr": "-34*z**3 - 11*z",
"real_solutions": [
0
],
"source_dataset": "polynomial_equations",
"source_index": 26,
"variable": "z"
}
| 3
|
Find the real value(s) of s in the equation: 4*s**3 - 5*s = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-1.118, 0.0, 1.118
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "4*s**3 - 5*s",
"real_solutions": [
-1.118,
0,
1.118
],
"source_dataset": "polynomial_equations",
"source_index": 27,
"variable": "s"
}
| 3
|
Find the real value(s) of d in the equation: -24*d**3 - 8*d**2 + 14*d = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-0.9484, 0.0, 0.6151
|
{
"degree": 3,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "-24*d**3 - 8*d**2 + 14*d",
"real_solutions": [
-0.9484,
0,
0.6151
],
"source_dataset": "polynomial_equations",
"source_index": 28,
"variable": "d"
}
| 3
|
Solve the polynomial equation for real m:
-3*m**2 - 17*m - 15 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your final answer.
3. If there are no real values that satisfy the equation, report your answer as an empty string: ""
4. Format your answer based on the number of solutions:
- For 1 solution: a single decimal number
- For 2 solutions: two comma-separated decimal numbers
- For 3 or more solutions: all values as comma-separated decimal numbers
5. Round all decimal values to 4 decimal places (rounding down when the 5th decimal place is 5 or greater).
|
-4.5734, -1.0933
|
{
"degree": 2,
"difficulty": {
"degree": [
2,
3
],
"terms": [
3,
4
]
},
"num_terms": 4,
"polynomial_expr": "-3*m**2 - 17*m - 15",
"real_solutions": [
-4.5734,
-1.0933
],
"source_dataset": "polynomial_equations",
"source_index": 29,
"variable": "m"
}
| 3
|
End of preview. Expand
in Data Studio
README.md exists but content is empty.
- Downloads last month
- 34