Fields generated by roots of $x^n+ax+b$

Let $a$ and $b$ be integers such that $x^n+ax+b$ is an irreducible polynomial. We study the number fields ${f Q}[|theta]$,where $ heta$ is a root of the above trinomial. We show thatif $nge 5$, then given an algebraic number field ${f K}$of degree $n$, then there are at most finitely many pairs$(a,b)$ such that ${f K}={f Q}[ heta]$.