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2017 A6: Maximization of Quintic

Source:

January 29, 2017
2017algebra

Problem Statement

Suppose PP is a quintic polynomial with real coefficients with P(0)=2P(0)=2 and P(1)=3P(1)=3 such that ∣z∣=1|z|=1 whenever zz is a complex number satisfying P(z)=0P(z) = 0. What is the smallest possible value of P(2)P(2) over all such polynomials PP?
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