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If _$α$ and _$β$ are the roots of the equation _{$x^{2} - x + 1 = 0,$} then _{$α^{2009} + β^{2009} =$}

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Correct option is D

x2−x+1=0 ⇒x=1+1−42 x=1+3i2 α=12+i32. β=12−i32 α=cosπ3+isinπ3,β=cosπ3−isinπ3 α2009+β2009=2cos2009(π3) =2cos[668π+π+2π3]=2cos(π+2π3) =−2cos2π3=−2(−12)=1

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If α and β are the roots of the equation x2−x+1=0, then α2009+β2009=

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If _$α$ and _$β$ are the roots of the equation _{$x^{2} - x + 1 = 0,$} then _{$α^{2009} + β^{2009} =$}