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The Bring-Jerrard Quintic Equation, its Algebraic Solution by Expansion

Abstract

I present a method of solving the Bring-Jerrard quintic equation by expansion. The aim of this research is to contribute further to the knowledge of quintic equations. The quest for a formula for the quintic equation has preoccupied mathematicians for many centuries. The general quintic equation in its trinomial form is called the Bring-Jerrard quintic equation.

The Bring – Jerrard equation has two parameters. The objective of this presentation is to present the expansion method as a viable tool for solving quintic equations and higher degree polynomials. In this research I split the unknown quantity in the quintic equation into three unknowns and expand and subsequently contract to the lowest possible form. The contraction of the expanded form involves factoring out the three unknown quantities to give the equation a solvable form. Three simultaneous equations in the three unknowns are then formed from the expanded quintic equations. The solution of the three equations yields an algebraic solution of the Bring-Jerrard quintic equation.

Samuel Bonaya Buya

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