Quadratic Equation
A quadratic equation is an equation that has the highest power of the variable in the equation equal to 2 while the powers of the other variables are integers which are less than 2. The general form of quadratic equation is ax2 + bx + c = 0.

Case 1: When C = 0

Solve the following equation

X2 – 4 X = 0
X2+ 6X = 0
2X2 – 8X = 0
4X2 – 5X = 0
Solution:

X2 – 4X = 0
X ( X – 4) = 0

X = 0 or X – 4 = 0

X= 0 or X = 4

X2 + 6X = 0
X( X + 6) = 0

X = 0 or X + 6 = 0

X= 0 or X= – 6

4X2 – 5 x = 0
X(4X – 5) = 0

X = 0 or 4X – 5 = 0

X = 0 or 4 X = 5

X= 0 or X = 5/4

Case 2: When b = 0

X2 – Y2 = ( X + Y) (X – Y)
M2 – N2= ( M + N) (M – N)
a2 – b2 = ( a + b) ( a – b)
Example: Simplify the following

X2 – 4 = 0
X 2 – 25 = 0
16 X 2– 100= 0
4X2 – 81 = 0
X2 – 7= 0
X2+ 9 = 0
Solution

X2 – 4 = 0
X 2 – 2 2 = 0

(X + 2) (X – 2)= 0

(X + 2) = 0 or (X – 2) = 0

X = -2 or X= 2



X2 – 25 = 0
(X)2 – ( 5)2

( X + 5) ( X – 5) = 0

X + 5 = 0 or X – 5 = 0

X = – 5 or X = 5



16 X 2– 100= 0
( 4X) 2 – (20) 2 = 0

4X + 20 = 0 or 4X – 20= 0

4X = – 20 or 4X = 20

X= – 20/4 or X = 20/4

X = – 5/2 or X = 5/2
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