GATE Electrical Engineering (EE) 2021 Solved Papers

If $\mathit{p}\left(\mathit{z}\right)={\mathit{z}}^3+\left(1+\mathit{j}\right){\mathit{z}}^2\left(2+\mathit{j}\right)\mathit{z}+3$, where $\mathit{z}$ is complex number.
Since, coefficients are complex numbers, therefore, all the roots cannot be real. Hence, option $\mathit{D}$ is correct.
Complex roots occur in conjugate pairs $\to$ false. Complex rootsoccur in conjugate pairs only if coefficients are all real nos.
Sum of the roots is real $\to$ false sum of all roots will be real number if complex roots occur in conjugate pairs. But their complex roots are not in conjugate pain.
$\overline{\mathit{P}\left(\mathit{z}\right)}=\mathit{P}\left(\overline{\mathit{z}}\right)$ is false statement.