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Question

If α is the non real root of x6=1 then α5+α3+α+1α2+1 is

A
α2
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B
α2
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C
α
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D
0
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Solution

The correct option is B α2
x6=1
For the given equation we know that sum of roots is equal to zero
1+α+α2+α3+α4+α5=0
α5+α3+α+1=α4α2(1)
Now,
α5+α3+α+1α2+1
=α4α2α2+1 (using (1))
=α2(α2+1)α2+1
=α2

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