Question

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

2(a² + b²)x² + 2(a + b)x + 1 = 0

Answer 1

The given equation is

2(a² + b²)x² + 2(a + b)x + 1 = 0

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

where a = 2(a² + b²), b = 2(a + b), c = 1

Therefore the discriminant

D = b² - 4ac

= (2(a + b))² - 4 x (2(a² + b²)) x (1)

= 4(a + b)² - 8a² - 8b²

= 4(a² + b² + 2ab) - 8a² - 8b²

= 4a² + 4b² + 8ab - 8a² - 8b²

= 8ab - 4a² - 4b²

∵ D < 0,

∴ The roots of the given equation are not real.