{"status": "success", "data": {"description_md": "There are real numbers $a, b, c, $ and $d$ such that $-20$ is a root of $x^3 + ax + b$ and $-21$ is a root of $x^3 + cx^2 + d.$ These two polynomials share a complex root $m + \\sqrt{n} \\cdot i,$ where $m$ and $n$ are positive integers and $i = \\sqrt{-1}.$ Find $m+n.$\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": "

There are real numbers $a, b, c, $ and d such that -20 is a root of x^3 + ax + b and -21 is a root of x^3 + cx^2 + d. These two polynomials share a complex root m + \\sqrt{n} \\cdot i, where m and n are positive integers and i = \\sqrt{-1}. Find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2021 AIME II Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/21_aime_II_p05", "prev": "/problem/21_aime_II_p03"}}