Let \( f(x)=a+b x+c x^{2} \) and \( \omega \neq 1 \) be a cube root...

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Let \( f(x)=a+b x+c x^{2} \) and \( \omega \neq 1 \) be a cube root of unity, and
\[
\Delta=\left|\begin{array}{lll}
a & b & c \\
b & c & a \\
c & a & b
\end{array}\right|
\]
then factors of \( \Delta \) are
(a) \( f(1) \)
(b) \( f(\omega) \)
(c) \( f\left(\omega^{2}\right) \)
(d) \( f(i) \).
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