difficulty int64 | source string | domain string | conversations list |
|---|---|---|---|
null | ai2-adapt-dev/openmath-2-math | math | [
{
"from": "human",
"value": "Determine the sum of the squares of the roots of the equation\n\n$$x^3 + x^2 + 2x - 20 = 0$$\n\ngiven that one of the roots is a complex number of the form $x = a + bi$, where $a$ and $b$ are integers."
},
{
"from": "gpt",
"value": "<think> Okay, so I have to find th... |
null | ai2-adapt-dev/openmath-2-math | math | [
{
"from": "human",
"value": "In a triangle, the square of the length of the median to one side is equal to the product of the lengths of the segments into which it divides the opposite side. If the length of the median is 12 cm, and the lengths of the segments are in the ratio 2:3, find the area of the tria... |
null | ai2-adapt-dev/openmath-2-math | math | [
{
"from": "human",
"value": "Find the product of the real roots of the polynomial $f(x) = x^4 - 6x^3 + 11x^2 - 6x - 1$."
},
{
"from": "gpt",
"value": "<think> Okay, so I need to find the product of the real roots of the polynomial f(x) = x⁴ - 6x³ + 11x² - 6x - 1. Hmm, let me start by recalling s... |
null | ai2-adapt-dev/openmath-2-math | math | [
{
"from": "human",
"value": "In the figure, $ABCD$ is a rectangle with $AD = 4$ and $CD = 6$. The diagonals $\\overline{AC}$ and $\\overline{BD}$ intersect at $O$, and $\\triangle AOB$ is folded over $\\overline{AB}$ so that point $O$ coincides with point $P$ on $\\overline{AD}$. If $\\overline{OP} \\perp \... |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"A sphere is inscribed in a right circular cylinder with radius 8 and heigh(...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"A square and a regular triangle share a common side. Each side of the squa(...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"Let $\\textbf{A} = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}$ and $(...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"Suppose $f(x)$ is a linear function such that $f(f(f(x)))=x$ for all real (...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"A positive number is 10 less than its cube root multiplied by 15. What is (...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"Three cylindrical cans have volumes of 50, 150, and 300 cubic centimeters.(...TRUNCATED) |
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