# An iterative approach for real roots of polynomials

## TL;DR

This paper introduces an iterative method to determine the conditions on polynomial coefficients that guarantee the existence of only distinct real roots, enhancing root-finding accuracy.

## Contribution

It provides necessary and sufficient coefficient conditions for polynomials to have exclusively distinct real roots, a novel theoretical insight.

## Key findings

- Derived explicit coefficient conditions for real roots
- Ensured roots are distinct and real under these conditions
- Improved understanding of polynomial root structure

## Abstract

In the present study, we propose necessary and sufficient assumptions on the coefficients in order to only get distinct real roots of polynomials.