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If alpha, beta in C are distinct roots o...

If `alpha, beta in C` are distinct roots of the equation `x^2-x+1=0` then `alpha^(101)+beta^(107)` is equal to

A

`-1`

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `alpha, beta` are the roots of `x^(2)-x+=0`
`therefore "Roots of" `x^(2)-x+1=0 are -omega,-omega^(2)`
`therefore` Let `alpha=-omega and beta=- omega^(2)`
`omega`impliesalpha^(101)+beta^(107)=(-omega)^(101)+(-omega^(2))^(107)=-(omega^(101)+omega^(214))`
`=-(omega^(2)+omega)" "[becauseomega^(3)=1]`
`=-(-1)" "[because1+omega+omega^(2)=0]=1`
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