Let \( f(x)=\left|\begin{array}{ccc}1 & 1 & 1 \\ 3-x & 5-3 x^{2} & 3 x^{3}-1 \\ 2 x^{2}-1 & 3 x^...

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Let \( f(x)=\left|\begin{array}{ccc}1 & 1 & 1 \\ 3-x & 5-3 x^{2} & 3 x^{3}-1 \\ 2 x^{2}-1 & 3 x^{5}-1 & 7 x^{8}-1\end{array}\right| \). Then, the equation \( f(x)=0 \) has
(a) no real root
(b) atmost one real root
(c) at least two real roots
(d) exactly one real root in \( (0,1) \) and no other real root
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