show that every irreducible polynomial on $\mathbb{F}_q[x] $ is separable

Question

I have already been able to show that if the irreducible polynomial $ f $ has degree n, then its roots are $ a, a^q \ldots, a^{q^{n-1}}$, where $ a $ is a roots of $ f $ to some extent.

How can I show that they are all different?