Contents

Introduction

Solving Simple Equations

Formulae

Factorising Quadratic Equations

Completing the Square method

General Solution method

Problem Solving

Quiz 

Algebra Main Page

General Solution of a Quadratic Equation

The general solution of an equation is as follow:

It can be used to solve any quadratic equation of the form ax² + bx + c

Example 1

Solve x² + 2x - 10 = 0

a = 1, b = 2 and c = -10                               first determine what a, b & c are 

Example 2

Solve 3x² - 5x +2 = 0.

Example 3

Solve 3x² - 9x + 2 = 0

is an imaginary number, thus there is no real roots for this equation.

Study the above three examples carefully, we note that the nature of the roots of a quadratic equation depends on b² - 4ac, which is known as the discriminant of the equation.

(1) If b² - 4ac > 0, then the equation has two real and distinct (or different) roots. See example 1.

(2) If b² - 4ac = 0, then the equation has two real and repeated roots that are real (only one answer). See example 2.

(3) If b² - 4ac < 0, then the equation has no real roots, i.e. the roots are complex. See example 3.