If ω is a cube root of unity, then a root of the following equation x+1ωω2ωx+ω21ω21x+ω=0 is

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x=1

x=ϖ

x=ϖ2

x=0

answer is D.

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Detailed Solution

Operate C1+C2+C3 we get, x+1+ω+ω2ωω2x+1+ω+ω2x+ω21x+1+ω+ω21x+ω=0⇒xωω2xx+ω21x1x+ω=0 ∵1+ω+ω2=0⇒x1ωω21x+ω2111x+ω=0⇒x=0

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