1) If α,β ∈ C are the distinct roots of the equation x2−x+1=0, , then α101+β107 is equal to A) -1 B) 0 C) 1 D) 2 Answer: Option CExplanation:We have, α,β are the roots of the x2-x+1=0, ∴ Roots of x2−x+1=0 and −ω,−ω2 ∴ Let α=−ω and β=−ω2 ⇒ α101+β107=(−ω)101+(−ω2)107 = −(ω101+ω214) = −(ω2+ω) ( ∵ ω3=1) = - ( -1) [ ∵ 1+ω+ω2=0 ] = 1