A simplified expression for the solution of cubic polynomial equations using function evaluation

TL;DR

This paper introduces a simplified method for solving cubic equations that relies solely on function and derivative evaluations at a single point, removing the need for coefficient manipulation and substitutions.

Contribution

It presents a novel approach that expresses cubic solutions directly through function evaluations, simplifying the traditional solving process.

Findings

Solution expressed solely in terms of function and derivative evaluations

Eliminates need for coefficient manipulation and substitutions

Simplifies solving cubic equations for easier understanding and recall

Abstract

This paper presents a simplified method of expressing the solution to cubic equations in terms of function evaluation only. The method eliminates the need to manipulate the original coefficients of the cubic polynomial and makes the solution free from such coefficients. In addition, the usual substitution needed to reduce the cubic equation is implicit in that the final solution is expressed in terms only of the function and derivative values of the given cubic polynomial at a single point. The proposed methodology simplifies the solution to cubic equations making them easy to remember and solve.