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Question
Write the quadratic equation whose roots are ‒2 and ‒3.
Solution
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 + α β = 0
i.e. x2 – (–5)x + 6 = 0
i.e. x2 + 5x + 6 = 0
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