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a_1^2 > 2ka_2/(k-1) if a polynomial had k distinct real roots

Source: 1994 Swedish Mathematical Competition p5

April 2, 2021

algebrapolynomial

Problem Statement

The polynomial

x^k + a_1x^{k-1} + a_2x^{k-2} +... + a_k

has

k

distinct real roots. Show that

a_1^2 > \frac{2ka_2}{k-1}