Question

Determine the nature of the roots of the following quadratic equation:

9a²b²x² – 24abcdx + 16c²d² = 0, a ≠ 0, b ≠ 0

Answer 1

The given equation is

9a²b²x² - 24abcdx + 16c²d² = 0

The given equation is on the form of ax² + bx + c = 0

Where a = 9a²b², b = -24abcd, c = 16c²d²

Therefore, the discriminant

D = b² - 4ac

= (-24abcd)² - 4 × (9a²b²) × (16c²d²)

= 576a²b²c²d² - 576a²b²c²d²

= 0

∵ D = 0

∴ The roots of the given equation are real and equal.