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Easy polynomial problem

Source: Tuymaada 2012, Problem 2, Day 1, Seniors

July 20, 2012
algebrapolynomialquadraticsinequalitiessum of rootsalgebra unsolved

Problem Statement

Let P(x)P(x) be a real quadratic trinomial, so that for all x∈Rx\in \mathbb{R} the inequality P(x3+x)≥P(x2+1)P(x^3+x)\geq P(x^2+1) holds. Find the sum of the roots of P(x)P(x).
Proposed by A. Golovanov, M. Ivanov, K. Kokhas
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