If α , β ∈ C are the distinct roots of the equation x 2 - x + 1 = 0 , then α 101 + β 107 is equal to

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Question: Answered & Verified by Expert

If

α, β \in C

are the distinct roots of the equation

x^{2} - x + 1 = 0,

then

α^{101} + β^{107}

is equal to

MathematicsComplex NumberJEE Main

Options:

A $2$
B $- 1$
C $0$
D $1$

Solution:

1324 Upvotes Verified Answer

The correct answer is:

1

x^{2} - x + 1 = 0

Roots are

- ω, - ω^{2}

α^{101} + β^{107} = {(- ω)}^{101} + {(- ω^{2})}^{107}

= - ω^{2} - ω

= 1

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