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Sum of common roots of the equations z^(...

Sum of common roots of the equations `z^(3) + 2z^(2) + 2z + 1 =0` and `z^(1985) + z^(100) + 1=0` is

A

`-1`

B

1

C

0

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
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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