{"status": "success", "data": {"description_md": "For certain real values of $a, b, c,$ and $d,$ the equation $x^4+ax^3+bx^2+cx+d=0$ has four non-real roots. The product of two of these roots is $13+i$ and the sum of the other two roots is $3+4i,$ where $i=\\sqrt{-1}.$ Find $b.$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>For certain real values of <span class=\"katex--inline\">a, b, c,</span> and <span class=\"katex--inline\">d,</span> the equation <span class=\"katex--inline\">x^4+ax^3+bx^2+cx+d=0</span> has four non-real roots. The product of two of these roots is <span class=\"katex--inline\">13+i</span> and the sum of the other two roots is <span class=\"katex--inline\">3+4i,</span> where <span class=\"katex--inline\">i=\\sqrt{-1}.</span> Find <span class=\"katex--inline\">b.</span></p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "1995 AIME Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/95_aime_p06", "prev": "/problem/95_aime_p04"}}