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

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.

To appear in "The Mathematical Gazette"; one remark is removed and some minor change