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IMC 2014, Problem 3

Source: IMC 2014

July 27, 2016
IMCalgebrapolynomialcollege contestsreal analysis

Problem Statement

Let nn be a positive integer. Show that there are positive real numbers a0,a1,…,ana_0, a_1, \dots, a_n such that for each choice of signs the polynomial ±anxn±an−1xn−1±⋯±a1x±a0\pm a_nx^n\pm a_{n-1}x^{n-1} \pm \dots \pm a_1x \pm a_0 has nn distinct real roots.
(Proposed by Stephan Neupert, TUM, München)
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