If α and β are the roots of equation x2 – 2x + 4 = 0, then what is the equation whose roots are α3/β2 and β3/α2?
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Correct answer: C
Explanation
The correct answer is option 3 (i.e. x2 – 2x + 4 = 0)
In x2 – 2x + 4 = 0
α + β = 2; αβ = 4
α3 + β3 = (α + β)3 – 3αβ (α + β)
= 8 – 3 × 4 (2)
= 8 – 24 = –16
α3 + β2 = (α + β)2 – 2αβ
= 4 – 2 × 4
= –4
α5 + β5 = (α3 + β3) (α2 + β2) – (αβ)2 (α + β)
= (–16) (–4) – 16 × 2
= 32
Sum of roots = 
Product of roots = 
= α.β = 4
x2 – 2x + 4 = 0