Suppose p(x) is an irreducible polynomial over Q of degree n, with integer coefficients. If p(x) has two roots r1 and r2 satisfying r1r2 = 5, prove that n is even.
Attempt at solution:
Because the base field is Q, the field extension is separable, hence no roots of multiplicity > 1.
Because r1r2 = 5, I think we can show that if the degree of n is odd, then this will contradict the fact that p(x) has integer coefficients somehow, but I can't seem to do this.
Any help would be appreciated very much, thank you.