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

If α, β∈C are the distinct roots of the equation x2-x+1=0, then α101+β107 is equal to
  1. 2
  2. -1
  3. 0
  4. 1

Solution

x2-x+1=0

Roots are -ω, -ω2.

α101+β107=-ω101+-ω2107

=-ω2-ω ∵ω3=1

=-ω2+ω

=1 ∵1+ω+ω2=0

Asked in: JEE Main 2018 (08 Apr)

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