# Math Guide

INTRODUCTION

QUADRATIC EQUATION: Anequation which has the unknown quantity raised only to powers which arewhole numbers and the highest power being the square of the unknown quantity is called a quadratic equation.

The most general form of a quadratic equation is ax2+bx+c=0.(where a not equal to zero)

Quadmeans two. So there are two values of x that satisfy such a quadratic equation.These values are called the roots of the quadratic equation.

My forthcoming post is on  , will give you more understanding about Algebra.

## Nature of the quadratic equation roots

How to determine the nature of the roots if quadratic equation is given? The answer is by using an important term "DESCRIMINANT".

Descriminant: b2-4ac determines the nature of roots of the quadratic equation

The nature of the roots of a quadratic equation is as follows :

-the roots are real and equal ,if b2-4ac=0.

-the roots are rational and unequal,if b2-4ac is positive and a perfect square.

-the roots are irrational ,if b2-4ac is positive but not a perfect square.

-the roots are imaginary,if b2-4ac<0.

## Example to find the nature of roots of a quadratic equation

Example 1: Determine the nature of roots of  X2+2x+1=0.

Solution: Here a="1,b=2" and c="1

Descriminant:b2-4ac= 22- 4*1*1 =4 - 4 =0.

So, the roots are real and equal.

Example 2: Determine the nature of roots of  X2-1=0.

Solution: Here a="1,b=0" and c = -1

Discriminant  b2-4ac = 02-4*1*-1= 4

So the roots are rational and unequal , since 4 is  positive and a perfect square.

Example 3:Determine the nature of roots of 2X2-4X+1.

Solution:Here a="2," b="-4" and c =1

Descriminant : b2-4ac =(-4)2 - 4*2*1 = 16 - 8="8.

So the roots are irrational ,since 8 is positive but not a perfect square.

Example 4:Determine the nature of roots of  X2+4x+5.

Solution:Here a =1,b=4,c=5

Discriminant: b2-4ac =42-4*1*5=16-20 = -4.

So the roots are imaginary,since -4 <0.