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Question

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

A
x2+2x16=0
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B
x2+2x+15=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 C x2+2x8=0
Given that, α+β=2 and α3+β3=56

(α+β)(α2+β2αβ)=56

2(α2+β2αβ)=56

α2+β2αβ=28

Also, (α+β)2=(2)2

α2+β2+2αβ=4

28+αβ+2αβ=4

28+3αβ=4

3αβ=24

αβ=8

Required equation is x2+2x8=0

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