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IMC 1995 Problem 9

Source: IMC 1995

February 19, 2021
algebrapolynomialcomplex analysis

Problem Statement

Let all roots of an nn-th degree polynomial P(z)P(z) with complex coefficients lie on the unit circle in the complex plane. Prove that all roots of the polynomial 2zP′(z)−nP(z)2zP'(z)-nP(z) lie on the same circle.
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