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2013 AIME II Problems/Problem 12

Revision as of 17:54, 4 April 2013 by Yrushi (talk | contribs) (Problem 12)
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Let $S$ be the set of all polynomials of the form $z^3 + az^2 + bz + c$, where $a$, $b$, and $c$ are integers. Find the number of polynomials in $S$ such that each of its roots $z$ satisfies either $|z| = 20$ or $|z| = 13$.

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