If x is a root of the polynomial
$x^m + c\_1 x^{m-1} +c\_2x^{m-2}+\cdots+c\_m = 0$
(with the coefficients $c\_1,c\_2,\ldots,c\_m$ all integers), then $x$ is either an integer or irrational.

My professor posed this question in class a few days ago. I'm not sure how to prove it. He told me to assume $a/b$ is a root of the polynomial and that a and b are relatively prime. I'm not sure how that helps.