On the discriminant of a trinomial
type: Item
instance of: scholarly article
title: On the discriminant of a trinomial
zbMATH Open document ID: 0552.12013
DOI: 10.1016/0024-3795(84)90089-2
author: Gary R. Greenfield
author: Daniel Drucker
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: \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.
Mathematics Subject Classification ID: 12E05
zbMATH DE Number: 3879047
zbMATH Keywords: discriminant of trinomial
zbMATH Keywords: resultant
MaRDI profile type: Publication
full work available at URL: 0024-3795(84)90089-2
OpenAlex ID: W2004814677
cites work: Algebraic coding theory
cites work: Graphical Evaluation of Sparse Determinants
cites work: Polynomials with PSL(2,7) as Galois group
cites work: Q5588717
cites work: On the Galois groups of cubics and trinomials
cites work: The admissibility of \(A_5\)
cites work: Some Remarks on Computing Galois Groups
cites work: Factorization of polynomials over finite fields
description: scientific article; zbMATH DE number 3879047