Question

Solve the following quadratic equation:

4x² – 2(a² + b²)x + a²b² = 0

Answer 1

Given:

4x² – 2(a² + b²)x + a²b² = 0

⇒ 4x² – 2a²x – 2b²x + a²b² = 0 

⇒ 2x(2x – a²) – b²(2x – a²) = 0 

⇒ (2x – b²) (2x – a²) = 0 

⇒ 2x – b² = 0 or 2x – a² = 0 

⇒ `x = b^2/2` or `x = a^2/2` 

Hence, the roots of the equation are `b^2/2` and `a^2/2`.