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Question

lf α+β=2 and α3+β3=56, then the quadratic equation whose roots are α, β, is:

A
x2+2x16=0
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B
x2+2x15=0
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C
x2+2x12=0
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D
x2+2x8=0
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Solution

The correct option is A x2+2x8=0
Given, (α+β)=2, α3+β3=56
(α+β)(α2+β2αβ)=56
(α+β)23αβ=28
43αβ=28
αβ=8
x2(α+β)x+αβ=0
x2+2x8=0

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