Accurate algebraic formula for the quintic & Solution by iteration of radicals
General Mathematics
2021-01-15 v1
Abstract
According to the Abel-Ruffini theorem [1] and Galois theory [2], there is no solution in finite radicals to the general quintic equation. This article takes a different approach and proposes a new method to solve the quintic by iteration of radicals. But, the most intriguing result is an accurate algebraic formula for absolute and relative root approximation: |formula - root| < 0.00432 and |formula/root - 1| < 0.0251. We then expand some of the geometric properties discussed to construct a trigonometric algorithm that derives all roots.
Keywords
Cite
@article{arxiv.2101.05610,
title = {Accurate algebraic formula for the quintic & Solution by iteration of radicals},
author = {Abdel Missa and Chrif Youssfi},
journal= {arXiv preprint arXiv:2101.05610},
year = {2021}
}