Math Guide

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 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 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: 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.