Question

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

(b + c)x² - (a + b + c)x + a = 0

Answer 1

The given equation is (b + c)x² - (a + b + c)x + a = 0

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

where a = (b + c), b = -(a + b + c), c = a

Therefore, the discriminant

D = b² - 4ac

= (-(a + b + c))² - 4 x (b + c) x (a)

= (a + b + c)² - 4ab - 4ac

= a² + b² + c² + 2ab + 2bc + 2ca - 4ab - 4ac

= a² + b² + c² - 2ab + 2bc - 2ac

∵ D > 0

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