ISI 2006 ME 1

[Cermank]

Question number 8. I just can't understand how to approach this question:



Any hint would be appreciated.

[dream theater]

all you have to do is solve the determinant

[Cermank]

Where does the x^3 fit in? Do I use it as a constant and introduce it in the matrix or something?

[Rajat]

You can put x=1 and solve it..
In fact, the roots of x are 1, omega and omega square
Also, 1+omega+omega square= 0