Let $\alpha$ and $\beta$ be the roots of the equation $x^{2}+x+1=0$ $\begin{array}{ll}\therefore & \alpha+\beta=-1 \text { and } \alpha \beta=1 \\ \Rightarrow & \alpha=\omega \text { and } \beta=\omega^{2} \\ (\because & \left.\omega^{3}=1,1+\omega+\omega^{2}=0\right)\end{array}$
option a, $b, c$ does not sat isfies the eqn $x^{2}-x+1=0$ Hence, option (d) is correct.