Question

The common roots of the equations $z^3+2z^2+2z+1=0$ and $z^{1985}+z^{100}+1=0$ are

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is C

We have, $z^3+2z^2+2z+1=0$
$\Rightarrow (z+1)(z^2+z+1)=0$
Its roots are $-1,\omega and{\omega }^2$. The root z=-1 does not satisfy the equation $z^{1985}+z^{100}+1=0$ but $z={\omega }^2$ satisfy it. Hence, $\omega$ and ${\omega }^2$ are the common roots.