Question

Solve the following quadratic equations by factorization: a²b²x²+b²x-a²x-1=0

Answer 1

SOLUTION :  

Given : a²b²x² + b²x - a²x - 1 = 0

b²x(a²x + 1) - 1(a²x + 1) = 0

(b²x - 1) (a²x + 1) = 0

(b²x - 1)  = 0  or  (a²x + 1) = 0

[Equate each factor to zero]

b²x = 1  or  a²x = - 1  

x = 1/b²  or  x = - 1/a²

Hence, the roots of the quadratic equation a²b²x² + b²x - a²x - 1 = 0 are 1/b²  & - 1/a² .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Solution :

Given Quadratic equation :

a²b²x² + b²x - a²x - 1 = 0

=> b²x( a²x + 1 ) - 1( a²x + 1 ) = 0

=> ( a²x + 1 )( b²x - 1 ) = 0

=> a²x + 1 = 0 or b²x - 1 = 0

=> a²x = -1 or b²x = 1

=> x = -1/a² or x = 1/b²

Therefore ,

x = -1/a² or x = 1/b²

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