Problem

Source: Indonesian MO (INAMO) 2020, Day 1, Problem 2

Tags: quadratics, algebra, polynomial, 2020, Indonesia MO, Indonesian MO



Problem 2. Let $P(x) = ax^2 + bx + c$ where $a, b, c$ are real numbers. If $$P(a) = bc, \hspace{0.5cm} P(b) = ac, \hspace{0.5cm} P(c) = ab$$then prove that $$(a - b)(b - c)(c - a)(a + b + c) = 0.$$