Solving Quadratic Equations

7

8.1 Introduction

EMBAF

In Grade 10, the basicsof solving linear equations, quadratic equations, exponential equationsand

linear inequalities werestudied. This chapter extends that work by looking at different methods for

solving quadratic equations.

See introductory video:VMemp at http://www.everythingmaths.co.za

7.2 Solution by Factorisation EMBAG

How to solve quadraticequations by factorisation was discussed in Grade 10. Here is an example to

remind you of what is involved.

Example 1: Solution of QuadraticEquations

QUESTION

Solve the equation 2 x^2 − 5 x− 12 = 0.

SOLUTION

Step 1 : Determine whether theequation has common factors

This equation has no common factors.

Step 2 : Determine if the equation is in the form ax^2 + bx + c with a > 0

The equation is in the required form, with a = 2, b =− 5 and c =− 12.

Step 3 : Factorise the quadratic

2 x^2 − 5 x− 12 has factors of the form:

(2x + s)(x + v)

with s and v constants to be determined. This multiplies outto

2 x^2 + (s + 2v)x + sv