Question

If $a\epsilon R$ such that $z=-i$ is a root for the polynomial $P\left(z\right)=z^3-z^2+z+1+a$, then the value of $a$ is $-2$.

• A. True
• B. False

Answer 1

The correct option is A True

If $z=-i$, then $z^2=-1,z^3=i$, and $P(-i)=i+1-i+1+a=2+a$.

Then,

$-i$ is a root for $P$ if and only if $a=-2$.

Hence, this is the answer.