{"status": "success", "data": {"description_md": "*This is a user suggested problem. The TopsOJ staff thanks and gives full credit to [ ianpark](https://www.topsoj.com/users/ianpark/profile) for their contribution.*\n\n****\n\nFor a general depressed cubic $f(x) = x^3+px+q=0$ with one real root and real coefficients, let us denote the real root as $r$ and one imaginary root as $a+bi$, where $a, b \\in \\mathbb{R}$. Given that $r$ can be written as $Kp+Lq+Ma+Nb$, such that $K, L, M, N \\in \\mathbb{R}$, compute $|K+L+M+N|$.", "description_html": "<p><em>This is a user suggested problem. The TopsOJ staff thanks and gives full credit to <a href=\"https://www.topsoj.com/users/ianpark/profile\"> ianpark</a> for their contribution.</em></p>&#10;<hr/>&#10;<p>For a general depressed cubic <span class=\"katex--inline\">f(x) = x^3+px+q=0</span> with one real root and real coefficients, let us denote the real root as <span class=\"katex--inline\">r</span> and one imaginary root as <span class=\"katex--inline\">a+bi</span>, where <span class=\"katex--inline\">a, b \\in \\mathbb{R}</span>. Given that <span class=\"katex--inline\">r</span> can be written as <span class=\"katex--inline\">Kp+Lq+Ma+Nb</span>, such that <span class=\"katex--inline\">K, L, M, N \\in \\mathbb{R}</span>, compute <span class=\"katex--inline\">|K+L+M+N|</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Depressed Cubic Roots", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}