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Question
The roots of the equation x2 + 6x – 4 = 0 are α, β. Find the quadratic equation whose roots are α2 and β2
Solution
If the roots are given, the quadratic equation is x2 – (sum of the roots)x + product the roots = 0.
For the given equation.
x2 + 6x – 4 = 0
α + β = – 6
αβ = – 4
α2 + β2 = (α + β)2 – 2αβ
= (– 6)2 – 2(– 4) = 36 + 8 = 44
α2β2 = (αβ)2 = (– 4)2 = 16
∴ The required equation is x2 – 44x – 16 = 0.
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