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Question

The common roots of the equations x3+2x2+2x+1=0 and x+x2+x3=0 are ( ω is non real cube root of unity)

A
ω,ω2
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B
1
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C
ω+ω2
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D
1
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Solution

The correct option is A ω,ω2
The roots of x+x2+x3=0 are 0,ω,ω2
Let f(x)=x3+2x2+2x+1
f(0)=1
f(ω)=1+2ω2+2ω+1=0
f(ω2)=1+2ω+2ω2+1=0
Hence, ω and ω2 are common roots of both the equations.

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