Problem

Source: Indonesia National Math Olympiad 2022 Problem 2 (INAMO 2022/2)

Tags: algebra, polynomial, number theory, Indonesia, Indonesia MO



Let $P(x)$ be a polynomial with integer coefficient such that $P(1) = 10$ and $P(-1) = 22$. (a) Give an example of $P(x)$ such that $P(x) = 0$ has an integer root. (b) Suppose that $P(0) = 4$, prove that $P(x) = 0$ does not have an integer root.