Question

Obtain a quadratic equation whose roots are –3 and –7.

Answer 1

Given, roots of quadratic equation are –3 and –7.

Let, α = –3 and β = –7

∴ α + β = – 3 + (–7) = –3 – 7 = –10

And  αβ = (–3)(–7) = 21

∵ The quadratic equation is given by,

x² – (α + β)x + αβ = 0

∴ x² – (–10x) +21 = 0

x² + 10x + 21 = 0

Hence, x² + 10x + 21 = 0 is the required quadratic equation.