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