If-is-a-cube-root-of-unity-then-a-root-of-the-following-polynomial-is-determinant-x-1-2-x-2-1-2-1-x-

Question Number 15180 by arnabpapu550@gmail.com last updated on 08/Jun/17

If ω is a cube root of unity, then a root

of the following polynomial is

| \begin{matrix} x + 1 & ω & ω^{2} \\ ω & x + ω^{2} & 1 \\ ω^{2} & 1 & x + ω \end{matrix} |

Answered by ajfour last updated on 08/Jun/17

(x + 1) (x^{2} - x) - ω^{2} x + ω^{2} (ω - ω^{2} x - 1) = 0

x (x + 1) (x - 1) + x = 0

\Rightarrow x (x^{2} - 1 + 1) = 0

o r x^{3} = 0 \Rightarrow x = 0 .

Commented by arnabpapu550@gmail.com last updated on 08/Jun/17

Thank you sir .

Commented by arnabpapu550@gmail.com last updated on 08/Jun/17

Please solve 15191 no . question too .