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Question

Let α and β be the roots of the equation x2+x+1=0. The equation whose roots are α19, β7 is

A
x2 - x - 1 = 0
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B
x2 - x + 1 = 0
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C
x2 + x - 1 = 0
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D
x2 + x + 1 = 0
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Solution

The correct option is D x2 + x + 1 = 0

Give x2+x+1=0
x=12[1±i3]=12(1+i3),12(1i3)=ω,ω2
But α19=ω19=ω and β7=ω14=ω2.
Hence the equation will be same.


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