Solving Polynomial Equations

Introduction

Linear and quadratic equations, dealt within Sections 3.1 and 3.2, are members of a class of equations, called polynomial equations . These have the general form:

$a_{n} x^{n} + a_{n - 1} x^{n - 1} + \dots + a_{2} x^{2} + a_{1} x + a_{0} = 0$

in which $x$ is a variable and $a_{n}, a_{n - 1}, \dots, a_{2}, a_{1}, a_{0}$ are given constants. Also $n$ must be a positive integer and $a_{n} \neq 0$ . Examples include $x^{3} + 7 x^{2} + 3 x - 2 = 0, 5 x^{4} - 7 x^{2} = 0$ and $- x^{6} + x^{5} - x^{4} = 0$ . In this Section you will learn how to factorise some polynomial expressions and solve some polynomial equations.

Prerequisites

be able to solve linear and quadratic equations

Learning Outcomes

recognise and solve some polynomial equations

1 Multiplying polynomials together

2 Factorising polynomials and equating coefficients

3 Polynomial equations

4 Solving polynomial equations when one solution is known

5 Solving polynomial equations graphically