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MathNet 2019-part-06 — 184 problems (EN–VI) Question 26

Math Olympiad Vault · MathNet 2019-part-06 — 184 problems (EN–VI)

Question 26

Let $P(x)$ be a polynomial of degree $n \geq 2$ with rational coefficients such that $P(x)$ has $n$ pairwise different real roots forming an arithmetic progression. Prove that among the roots of $P(x)$ there are two that are also the roots of some polynomial of degree 2 with rational coefficients.