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Question
The roots of the equation x2 + 6x – 4 = 0 are α, β. Find the quadratic equation whose roots are α2β and β2α
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
α2β + β2α = αβ(α + β)
= – 4(– 6) = 24
α2β × β2α = α3β3 = (αβ)3 = (– 4)3 = – 64
∴ The required equation = x2 – 24x – 64 – 0
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