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The value of $x$, if $\left|\begin{array}{ccc}-x & 1 & 0 \\ 1 & -x & 1 \\ 0 & 1 & -x\end{array}\right|=0$ is equal to
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The correct answer is:
$\pm \sqrt{2}$
We have $\Delta=\left|\begin{array}{ccc}-x & 1 & 0 \\ 1 & -x & 1 \\ 0 & 1 & -x\end{array}\right|$
$\Delta=-x\left(x^2-1\right)-1(-x-0)=0 \Rightarrow x= \pm \sqrt{2}$
$\Delta=-x\left(x^2-1\right)-1(-x-0)=0 \Rightarrow x= \pm \sqrt{2}$
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