Bezoutians and the discriminant of a certain quadrinomials

TL;DR

This paper derives an explicit formula for the discriminant of a specific class of quadrinomials using Bezoutians, providing a new algebraic tool for analyzing polynomial roots.

Contribution

It introduces a novel explicit formula for the discriminant of quadrinomials of the form x^n + t(x^2 + ax + b) utilizing Bezoutians, advancing algebraic methods.

Findings

Explicit discriminant formula for the given quadrinomials

Application of Bezoutians to polynomial discriminants

Enhanced understanding of polynomial root structure

Abstract

We give an explicit formula for the discriminant $\Delta_f (x)$ of the quadrinomials of the form $f (x)=x^n+ t (x^2+ax+b)$. The proof uses Bezoutians of polynomials.