Question

The roots of the equation x² + 6x – 4 = 0 are α, β. Find the quadratic equation whose roots are α² and β²

Answer 1

If the roots are given, the quadratic equation is x² – (sum of the roots)x + product the roots = 0.

For the given equation.

x² + 6x – 4 = 0

α + β = – 6

αβ = – 4

α² + β² = (α + β)² – 2αβ

= (– 6)² – 2(– 4) = 36 + 8 = 44

α²β² = (αβ)² = (– 4)² = 16

∴ The required equation is x² – 44x + 16 = 0.