Maximum possible number of distinct real roots
Source: 2012 Balkan Shortlist (BMO) A3
April 5, 2020
Problem Statement
Determine the maximum possible number of distinct real roots of a polynomial of degree with real coefficients satisfying the condition
\begin{align*} P(a)^3 + P(b)^3 + P(c)^3 \geq 3 P(a) P(b) P(c) \end{align*}
for all real numbers with