MathLAB Journal

On Roots of Apolar Polynomials

Abstract

Kristofer Jorgenson

This article continues the exploration of methods based on that of Gian-Carlo Rota that involve
apolar invariants used for solving cubic and quintic polynomial equations.These polynomial invariants
were disclosed previously as an alternative to and to clarify the umbral method of Rota.Theorems
are proved regarding quintic, cubic, and quadratic polynomials that are pairwise apolar in that they
satisfy particular polynomial apolar invariants.