Show that the equation has no real roots, when .

Question

Philoid · Accepted Answer

For a quadratic equation, ax² + bx + c = 0,

D = b² – 4ac

If D < 0, roots are not real.

⇒ D = 4(a + b)² – 8(a² + b²)

⇒ D = 4a² + 4b² + 8ab – 8a² – 8b²

⇒ D = -4(a² + b² – 2ab) = -4(a – b)²

Thus, D < 0 for all values of a and b.

∴ Roots are not real.