Question

Without solving, comment upon the nature of roots of the following equation:

x² – ax – b² = 0

Answer 1

x² – ax – b² = 0

a = 1, b = –a and c = –b²

∴ Discriminant = b² – 4ac

= (–a)² – 4(1)(–b²)

= a² + 4b²

= a positive value

Since a² + 4b² is not a perfect square, roots are irrational

Since D > 0, then equation has two real and unequal roots.