If \[\omega \] is a cube root of unity, then a root of the equation \[\left| \begin{matrix} x+1 & \omega & {{\omega }^{2}} \\ \omega & x+{{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & x+\omega \\ \end{matrix} \right|=0\] is [MNR 1990; MP PET 1999]

If \[\omega \] is a cube root of unity, then a root of the equation

1.	If \[\omega \] is a cube root of unity, then a root of the equation \[\left\| \begin{matrix} x+1 & \omega & {{\omega }^{2}} \\ \omega & x+{{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & x+\omega \\ \end{matrix} \right\|=0\] is [MNR 1990; MP PET 1999]
A.	\[x=1\]
B.	\[x=\omega \]
C.	\[x={{\omega }^{2}}\]
D.	\[x=0\]
Answer» E.

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If \[\omega \] is a cube root of unity, then a root of the equation \[\left| \begin{matrix} x+1 & \omega & {{\omega }^{2}} \\ \omega & x+{{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & x+\omega \\ \end{matrix} \right|=0\] is [MNR 1990; MP PET 1999]

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