Contents

Introduction

Solving Simple Equations

Formulae

Factorising Quadratic Equations

Completing the Square method

General Solution method

Problem Solving

Quiz 

Algebra Main Page

Factorisating Quadratic Equations

The general form of a quadratic equation is ax² + bx + c = 0, where a, b and c are real numbers and a is not 0.

In the algebra of real numbers, if two numbers Y and Z are such that Y x Z = 0, then either Y = 0 or Z = 0 or both of them are equal to zero. We shall use this principle to solve quadratic equations.

Example 1

Solve x² - 3x - 28 = 0

(x - 7)(x + 4) = 0

x - 7 = 0 or x + 4 = 0

x = 7 or -4

Example 2

Solve 5x² + 15x = 0

(5x + 0)(x + 3) = 0

5x = 0 or x +3 =0

x = 0 or -3  

Example 3

Solve 4x² -25 = 0

(2x + 5)(2x - 5) = 0

2x + 5 = 0 or 2x - 5 = 0

x = 5/2