Discussion
If \(\begin{vmatrix} 1 & 0 & 0 \\ x & x+2 & 0 \\ x^{2} & x & x+3 \end{vmatrix} = 0\), then value of x are
Answer: C
The values are −2, −3.
The determinant is lower triangular (all entries above the diagonal are zero), so it equals the product of the diagonal entries:
\[ \begin{aligned} 1 \cdot (x + 2)(x + 3) &= 0 \\ &\Rightarrow x \\ &= -2 \text{ or } x \\ &= -3 \end{aligned} \]
The options 2, 3 and −2, 3 have the wrong signs, and no factor gives 1 or −1.
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