If \( a_{i}, b_{i}, c_{i} \in \mathbf{R}(i=1,2,3) \) and \( x \in \...
If \( a_{i}, b_{i}, c_{i} \in \mathbf{R}(i=1,2,3) \) and \( x \in \mathbf{R} \) and
\[
\Delta=\left|\begin{array}{lll}
a_{1}+b_{1} x^{2} & a_{1} x^{2}+b_{1} & c_{1} \\
a_{2}+b_{2} x^{2} & a_{2} x^{2}+b_{2} & c_{2} \\
a_{3}+b_{3} x^{2} & a_{3} x^{2}+b_{3} & c_{3}
\end{array}\right|=0
\]
then
(a) \( x=1 \)
(b) \( x=-1 \)
(c) \( \left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right|=\mathbf{O} \)
(d) \( x=0 \)
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