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The common roots of the equation Z^3+2Z^...

The common roots of the equation `Z^3+2Z^2+2Z+1=0` and `Z^1985+Z^100+1=0` are

A

`-1`

B

1

C

0

D

1

Text Solution

Verified by Experts

We have, `z^(3)+2z^(2)+2z+1=0`
`rArr (z^(3)+1)+2z(z+1)=0`
`rArr (z+1)(z^(2)+z+1)=0`
`rArrz=-1,omega,omega^(2)`
Since, `z=-1` does not satisfy `z^(1985)+z^(100)+1=0` while `z=omega, omega^(2)` satisfy it, hence, sum is `omega+omega^(2)=-`
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