The Cubic Equation Made Simple

Abstract

This article introduces an intuitive function MY that simplifies solving cubic equations without venturing into the complex space. To many, it's quite strange that cubic root(s) are expressed using trigonometric functions in the three-real-roots case versus real-radicals in the one-real-root case. Yet, the MY function provides a different perspective to this oddity and shows that the transition between the two worlds is actually smooth. Although MY's behavior resembles power functions, it cannot be expressed in real radicals. That said, we succeeded in proving an accurate closed form algebraic approximation of MY. So yes, casus irreducibilis still holds, but real radicals can get you very close!