How to Solve a Quadratic Equation – By Factoring

Last updated: December 16, 2011 by +Sarbjit

Hello Friends!!

Today we will learn how to solve Quadratic Equations. There are many methods to solve quadratic equations.  The easiest one is to factorize the Quadratic Equation.

We will learn how to factorize a quadratic equation to get the roots (Roots are the answers or solutions of a quadratic Equation. Quadratic Equations have two roots).

A general Quadratic Equation can be written as:

ax² + bx + c; where a, b and c are numbers.

Example:

Factorize x² + 5x + 6.

This is a quadratic equation with a = 1, b = 5 and c =6.

We will find the factors of '6' which when added give '5'. So the factors are 2 and 3.

2 x 3 = 6 (c)

2 + 3 = 5 (b)

So the equation can be written as

x² + 2x + 3x + 6 = 0

Solving this

x (x + 2) + 3 (x + 2) = 0 (Taking x common from the first two terms and 3 common from the last two)

(x + 2)  (x + 3) = 0 (Taking (x + 2) common.

This can only be true

iff x + 2 = 0 OR x + 3 = 0

iff x = - 2 OR x = -3

So the roots are -2 and -3.

In our next post we will learn how to solve difficult Quadratic

Equations.

Happy Learning!!

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