Expressions Relating to the Roots of a Polynomial

Introduction

You have aready seen several results for finding the values of expressions relating to the roots of a polynomial

Expressions and roots of polynomials

In addition to these you have also used the following results for the roots of quadratic equations:

Expressions and roots of polynomials

There are equivalent results to these for the roots of cubic and quartic equations

Example

Expressions and roots of polynomials

Sums of Squares

You can find an expression for the sum of the squares of a quartic equation in a similar way, by multiplying out (α + β + γ + δ)2

Expressions and roots of polynomials

You can find a similar result for the sum of the cubes of a cubic equation y multiplying out (α + β + γ)3

Expressions and roots of polynomials

Expressions and roots of polynomials