Question

Solve the following quadratic equations by factorization:
a²b²x²+b²x-a²-1=0

Answer 1

Solve the following quadratic equations by factorization:

a²b²x²+b²x-a²-1=0

x = -1/a², x = -1/b² are the roots.

Given,

a²b²x²+b²x-a²-1=0

⇒ b²x[a²x + 1] - 1[a²x + 1] = 0

⇒ [a²x + 1]  [b²x - 1] = 0

⇒ [a²x + 1] = 0, [b²x - 1] = 0

⇒ a²x = - 1, b²x = - 1

⇒ x = -1/a², x = -1/b²

Hence, x = -1/a², x = -1/b² are the roots of quadratic equation found by using factorization.