Let be a polynomial of degree with rational coefficients such that has pairwise distinct real roots forming an arithmetic progression. Prove that among the roots of there are two that are also roots of some degree polynomial with rational coefficients.
Let $P$ be a polynomial of degree $n \geq 2$ with rational coefficients such that $P$ has $n$ pairwise distinct real roots forming an arithmetic progression. Prove that among the roots of $P$ there are two that are also roots of some degree $2$ polynomial with rational coefficients.
Izvor: Srednjoeuropska matematička olimpijada 2018, ekipno natjecanje, problem 2
Školjka 
be a polynomial of degree 
with rational coefficients such that 
pairwise distinct real roots forming an arithmetic progression. Prove that among the roots of 
polynomial with rational coefficients.