Let $\displaystyle f(x),g(x)$ be polynomials with rational coefficients, and $\displaystyle f(x)$ is irreducible. Suppose further that there exists a complex number $\displaystyle \alpha$ such that $\displaystyle f(\alpha)=g(\alpha)=0$. Prove that $\displaystyle f(x)|g(x).$

I do not know how to prove. and I've thought it for many times....Would you help me out?