Revisiting the general cubic: A simplification of Cardano's solution

2022/04/15 by Liao, Hsin-Chieh, Shiue, Peter Jao-Shyong, Saul, Mark
#01A72 #97-02 #97H99 #FOS: Mathematics #History and Overview (math.HO)

paper · doi:10.48550/arxiv.2204.07507

Abstract

Motivated by the recent work of William Y.C. Chen, in which he presents a way to solve cubic equations by considering the identity of Sylvester, we investigate the solutions obtained in this way. It leads us to a unified expression of the solutions different from Cardano's formula. Plenty of examples are given in this paper, also some interesting identities are obtained as byproducts.

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