Accurate algebraic formula for the quintic & Solution by iteration of radicals

Abdel Missa; Chrif Youssfi

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arXiv · 2101.05610

Accurate algebraic formula for the quintic & Solution by iteration of radicals

Abdel Missa·Chrif Youssfi

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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.

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Abdel Missa, Chrif Youssfi. 2021-01-12. Accurate algebraic formula for the quintic & Solution by iteration of radicals. https://arxiv.org/abs/2101.05610

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