MathDB

1

Part of 2012 Serbia Team Selection Test

Problems(1)

Polynomial satisfying P(a)^3+P(b)^3+P(c)^3 >= 3P(a)P(b)P(c)

Source: Serbia Additional TST 2012, Problem 1

5/19/2012
Let P(x)P(x) be a polynomial of degree 20122012 with real coefficients satisfying the condition P(a)3+P(b)3+P(c)3≥3P(a)P(b)P(c),P(a)^3 + P(b)^3 + P(c)^3 \geq 3P(a)P(b)P(c), for all real numbers a,b,ca,b,c such that a+b+c=0a+b+c=0. Is it possible for P(x)P(x) to have exactly 20122012 distinct real roots?
algebrapolynomialfunctioninequalitiesabsolute valuealgebra proposed