MathDB
P (x) = P_0 (x) + xP_1 (x)( 1- x)P_2 (x)

Source: Austrian Polish 1991 APMC

May 1, 2020
polynomialalgebra

Problem Statement

Let P(x)P(x) be a real polynomial with P(x)≥0P(x) \ge 0 for 0≤x≤10 \le x \le 1. Show that there exist polynomials Pi(x)(i=0,1,2)P_i (x) (i = 0, 1,2) with Pi(x)≥0P_i (x) \ge 0 for all real x such that P(x)=P0(x)+xP1(x)(1−x)P2(x)P (x) = P_0 (x) + xP_1 (x)( 1- x)P_2 (x).
Back to ProblemsView on AoPS