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