M/F normal, determine whether there is an automorphism $\sigma\in Gal(M/F)$ with $\sigma(a)=a'$ and $\sigma(b)=b'$

Question

Let $M$ be a normal extension of $F$. Suppose that $a, a'$ are roots of $min(F,a)$ and that $b,b'$ are roots of $min(F,b)$,and that $min(F,a)\neq min(F,b)$. Determine whether or not there is an automorphism $\sigma\in Gal(M/F)$ with $\sigma(a)=a'$ and $\sigma(b)=b'$