2021 AIME II Problems/Problem 4

Revision as of 23:37, 22 March 2021 by Jimy (talk | contribs) (Solution)

Problem

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 $m+n.$

Solution 1

Conjugate root theorem

Solution in progress

~JimY

Solution 2

See also

2021 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
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All AIME Problems and Solutions

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