Root separation for reducible integer polynomials

TL;DR

This paper constructs parametric families of reducible monic polynomials with two roots extremely close, highlighting properties of root separation in such polynomials.

Contribution

It introduces new parametric families of reducible polynomials with closely spaced roots, advancing understanding of root separation phenomena.

Findings

Identifies specific polynomial families with minimal root separation

Demonstrates how reducibility affects root proximity

Provides insights into root clustering in reducible polynomials

Abstract

We construct parametric families of (monic) reducible polynomials having two roots very close to each other.