How to show that, the Galois Group is doubly transitive.

Question

Let $F$ be any algebraically closed field of characteristic $p\neq 2$. Let $x,s$ are independent variables. How to show that Galois group $G$ of a polynomial $f(x,s)$ is doubly transitive over F(s).

Things I have in hand is 1) $f(x,s)$ is irreducible and separable in the variable $x$.

Thank you.