Locating Complex Roots of Quintic Polynomials

Abstract

Since there are no general solutions to polynomials of degree higher than four, high school and college students only infrequently investigate quintic polynomials. Additionally, although students commonly investigate real roots of polynomials, only infrequently are complex roots – and, more particularly, the location of complex roots – investigated. This paper considers features of graphs of quintic polynomials and uses analytic constructions to locate the functions’ complex roots. Throughout, hyperlinked dynamic applets are provided for the student reader to experientially participate in the paper. This paper is an extension to other investigations regarding locating complex roots (Bauldry, Bossé, & Otey, 2017).