Question

If the roots of a quadratic equation are 4 and –5, then form the quadratic equation.

Answer 1

Let α = 4 and β = –5

α + β = 4 – 5 = –1

And α × β = 4 × (–5) = –20

∴ The required quadratic equation is

x² – (α + β)x + αβ = 0

∴ x² – (–1)x + (–20) = 0

∴ x² + x – 20 = 0