If ω is a cube root of unity, then a root of the equation is \(\left| {\begin{array}{*{20}{c}} {x + 1}&\omega &{{\omega ^2}}\\ \omega &{x + {\omega ^2}}&1\\ {{\omega ^2}}&1&{x + \omega } \end{array}} \right| = 0\)
1
x = ω
2
x = 0
3
x = 1
4
x = ω2
If ω is a cube root of unity, then a root of the equation is \(\left| {\begin{array}{*{20}{c}} {x + 1}&\omega &{{\omega ^2}}\\ \omega &{x + {\omega ^2}}&1\\ {{\omega ^2}}&1&{x + \omega } \end{array}} \right| = 0\)