A note about irreducibility of a resultant

TL;DR

This paper presents a theorem on the irreducibility of a polynomial resulting from the resultant of two polynomials, using field theory, and discusses the converse theorem with examples.

Contribution

It introduces a new theorem on the irreducibility of resultants and explores its converse, supported by examples and field theory-based proof.

Findings

The resultant of two polynomials can be irreducible under certain conditions.

A converse theorem relating to the irreducibility of resultants is established.

Examples illustrate the applicability of the theorems.

Abstract

We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.