Question

Write the quadratic equation whose roots are ‒2 and ‒3.

Answer 1

Let the roots be α = –2 and β = –3.

∴ α + β = (–2) + (–3) = –5 and αβ = (–2)(–3) = 6

Hence, the required quadratic equation is

x² – (α + β)x + αβ = 0

i.e., x² – (–5)x + 6 = 0

i.e., x² + 5x + 6 = 0