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Question

A quadratic equation whose roots are (γα)2 and (βα)2, where α,β,γ are the roots of x3+27=0 is

A
x2x+1=0
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B
x2+3x+9=0
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C
x2+x+1=0
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D
x23x+9=0
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Solution

The correct option is C x2+x+1=0
α,β,γ are the roots of x3+27=0
α=3,β=3ω,γ=3ω2
(γα)2=(3ω23)2=ω
(βα)2=(3ω3)2=ω2
Equation whose roots are ω,ω2 is x2+x+1=0
Hence, option C.

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