MathDB
Polynomial inequality

Source: 2019 MEMO Problem T-2

August 30, 2019
algebrapolynomialmemoMEMO 2019roots

Problem Statement

Let α\alpha be a real number. Determine all polynomials PP with real coefficients such that P(2x+α)(x20+x19)P(x)P(2x+\alpha)\leq (x^{20}+x^{19})P(x) holds for all real numbers xx.
Proposed by Walther Janous, Austria