$f(x)$ irreducible over $\mathbb Q$ of prime degree ; then Galois group of $f$ is solvable iff $L=\mathbb Q(a,b)$ for any two roots $a,b$ of $f$?

Question

Let $f(x)\in \mathbb Q[x]$ be irreducible polynomial of prime degree , $L$ be its splitting field , then how to show that $f(x)$ is solvable by radicals over $\mathbb Q$ iff $L=\mathbb Q(a,b)$ for any two roots $a,b$ of $f(x)$ ? i.e. how to show that $Gal(L/\mathbb Q)$ is solvable iff $L=\mathbb Q(a,b)$ for any two roots $a,b$ of $f(x)$ ?

EDIT : Any reference of book or article giving a full demonstration of the result is also highly appreciated