Q2 / 108 · NTA Abhyas (JEE Main) 2020 · Mathematics · Complex Number

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

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

Solution

x^{2} - x + 1 = 0

Roots are

- ω, - ω^{2}

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

= - ω^{2} - ω

= 1

Hence, the correct answer is option: 'D'.

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