On the discriminant of a trinomial
\textit{R. G. Swan} [Pac. J. Math. 12, 1099-1106 (1962; Zbl 0113.017)] proved that the trinomial \(f(x)=x^ n+ax^ k+b\) with \(0<k<n\) has discriminant \[ D(f)=(-1)^{n(n-1)/2}\quad b^{k-1}\quad [n^ N b^{N-K}-(-1)^ N (n-k)^{N-K} k^ K a^ N]^ d \] where \(d=(n,k)\), \(N=n/d\), \(K=k/d\). The authors obtain the above result by evaluating an associated resultant.
scientific article; zbMATH DE number 3879047