JAMB 1997 · UME · Q24

Find the non-zero positive value of $x$ which satisfies $\begin{vmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x \end{vmatrix} = 0$ .

Worked solution (try it first)

Expand along the first row: $x(x \cdot x - 1 \cdot 1) - 1(1 \cdot x - 1 \cdot 0) + 0$ .
This is $x^3 - x - x = x^3 - 2x$ , so $x(x^2 - 2) = 0$ .
So $x = 0$ or $x^2 = 2$ .
The non-zero positive value is $x = \sqrt2$ , option C.