{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"4085dd6a-4002-5d8f-9dd9-3c82b3833a78","task_key":"intermediate~5falgebra--test--4085dd6a-4002-5d8f-9dd9-3c82b3833a78","task_revision_id":"1","upstream_id":"","short_description":"The polynomial $f(x)=x^3-3x^2-4x+4$ has three real roots $r_1$, $r_2$, and…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The polynomial $f(x)=x^3-3x^2-4x+4$ has three real roots $r_1$, $r_2$, and $r_3$.  Let $g(x)=x^3+ax^2+bx+c$ be the polynomial which has roots $s_1$, $s_2$, and $s_3$, where\\n\\\\begin{align*}\\ns_1 &= r_1+r_2z+r_3z^2, \\\\\\\\\\ns_2 &= r_1z+r_2z^2+r_3, \\\\\\\\\\ns_3 &= r_1z^2+r_2+r_3z,\\n\\\\end{align*}and $z=\\\\frac{-1+i\\\\sqrt3}2$.  Find the real part of the sum of the coefficients of $g(x)$.\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}