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Solution of a Quadratic Equation by Factorisation

We should know the formulae given below:
(A + B)2 = A2 + B2 + 2AB
 (A - B)2 = A2 + B2 - 2AB
(A + B)2 = (A - B)2 + 4AB
(A - B)2 = (A + B)2 - 4AB
 A2 - B2 = (A + B) (A - B)
(A + B)3 = A3 + B3 + 3AB ( A + B)
(A - B)3 = A3 - B3 - 3AB (A - B)
A3 + B3 = (A + B)(A2 - AB + B2)
A3 - B3 = (A - B)(A2 + AB + B2)

We can factorize the quadratic equation ax2 + bx + c = 0; a 0, by 'splitting the middle term' method.

 

Example

Solve the equation for x,
x2 - 2x - 8 = 0

Solution

x2 - 2x - 8 = 0
  x2 - 4x + 2x - 8 = 0

 x(x - 4) + 2(x - 4) = 0
  (x - 4)(x + 2)=0

Hence, x - 4 = 0 (or) x + 2 = 0
       
  x = 4 , x = -2.


 

Example

Find the roots of the equations by factorisation
(a) x2 - 64 = 0              (b) x2 - 81 = 0

Solution

(a) x2 - 64 = 0
    (x)2 - (8)2=0
    (x + 8)(x - 8)=0
Hence, x + 8 = 0 or x - 8 = 0
Therefore, x = -8 , x =8.
(b) x2 - 81=0
  (x + 9)(x - 9)=0
Hence, x + 9 = 0 or x - 9 = 0  x = -9 , x = 9.

 





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