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

Options

A. `-1`
B. 1
C. 0
D. 1

Explanation

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)=-`