MathDB
A polynomial with rational coefficients

Source: MEMO 2018 T2

September 2, 2018
algebrapolynomialroots

Problem Statement

Let P(x)P(x) be a polynomial of degree n≥2n\geq 2 with rational coefficients such that P(x)P(x) has n n pairwise different reel roots forming an arithmetic progression .Prove that among the roots of P(x)P(x) there are two that are also the roots of some polynomial of degree 22 with rational coefficients .
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