Let \( \Delta=\left|\begin{array}{ccc}1 & x & x^{2} \\ x^{2} & 1 & x \\ x & x^{2} & 1\end{array}...

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Let \( \Delta=\left|\begin{array}{ccc}1 & x & x^{2} \\ x^{2} & 1 & x \\ x & x^{2} & 1\end{array}\right| \), then
(a) \( 1+x^{3} \) is a factor of \( \Delta \)
(b) \( \left(1-x^{3}\right)^{2} \) is factor of \( \Delta \)
(c) \( \Delta(x)=0 \) has 4 real roots
(d) \( \Delta(1)=1 \)
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