Find all polynomials $p$ with real coefficients such that for all real $x$ , $xp(x)p(1-x)+x^3 +100 \ge 0$.
Problem
Source: Slovenia TST 1997 p2
Tags: polynomial, functional, Functional inequality, algebra, inequalities
Source: Slovenia TST 1997 p2
Tags: polynomial, functional, Functional inequality, algebra, inequalities
Find all polynomials $p$ with real coefficients such that for all real $x$ , $xp(x)p(1-x)+x^3 +100 \ge 0$.