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# Determinant

0
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Find all values of x such that

$$\begin{vmatrix} x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x \end{vmatrix} = 0$$

Enter your values separated by commas.  For example, if you think the possible values are 4, 5, and 6, then enter your answer as "4,5,6".

May 14, 2022

If you simplify the determinant, the equation is just $$x^3 - 3x + 2 = 0$$. You can solve that by factorizing the left-hand side.