English

The roots of any polynomial equation

Classical Analysis and ODEs 2007-05-23 v2

Abstract

We provide a method for solving the roots of the general polynomial equation a[n]*x^n+a[n-1]*x^(n-1)+..+a1*x+a0=0. To do so, we express x as a powerseries of s, and calculate the first n-2 coefficients. We turn the polynomial equation into a differential equation that has the roots as solutions. Then we express the powerseries' coefficients in the first n-2 coefficients. Then the variable s is set to a0. A free parameter is added to make the series convergent.

Keywords

Cite

@article{arxiv.math/0408264,
  title  = {The roots of any polynomial equation},
  author = {Geert-Jan Uytdewilligen},
  journal= {arXiv preprint arXiv:math/0408264},
  year   = {2007}
}

Comments

3 pages

R2 v1 2026-07-22T17:08:54.230Z