Question

Find the roots of quadratic equations 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 = b²/2 or x = a²/2

Hence, the roots of the equation are b²/2 and a²/2