# Quadratic Learning

**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 ax ^{2}+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 Odd Numbers List and Multiplying Significant Figures , 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**: **b**^{2}**-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 equa**l ,if **b**^{2}**-4ac=0**.

*-*the roots are **rational and unequa**l,if **b**^{2}**-4ac **is positive and a perfect square.

*-*the roots are **irrational** ,if **b**^{2}**-4ac **is positive but not a perfect square.

*-the roots are imaginary,if b^{2}-4ac<0.*

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

Example 1: Determine the nature of roots of X^{2}+2x+1=0.

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

Descriminant:**b**^{2}**-4ac=** 2^{2}- 4*1*1 =4 - 4 =0.

So, the roots are **real and equa**l.

Example 2: Determine the nature of roots of X^{2}-1=0.

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

Discriminant **b**^{2}**-4ac** = 0^{2}-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 2X ^{2}-4X+1.*

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

*Descriminant : b^{2}-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 X ^{2}+4x+5.*

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

*Discriminant: b^{2}-4ac =4^{2}-4*1*5=16-20 = -4.*

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