Let $\displaystyle F$ be a field with characteristic 0.$\displaystyle E$is a finite field extension of $\displaystyle F$. Prove that $\displaystyle E$is a separable extension...

I know that for an $\displaystyle \alpha$, if the minimal polynomial $\displaystyle f(x)$ splits on $\displaystyle E$, then $\displaystyle f(x)$is separable on $\displaystyle E$. But why $\displaystyle f(x)$splits?