QuestionThe value(s) of $x$ for which $A=\left|\begin{array}{ccc}1 & 0 & 0 \\ 2 & 2 & 2 \\ 1 & x & x^{2}\end{array}\right|=0$ is (are) $x=2$ only $x=1$ only $x=0$ and $x=1$ $x=0$ and $x=2$ None of these

Studdy Solution
Determine which values of $x$ satisfy the equation:
The solutions are $x = 0$ and $x = 1$.
Thus, the correct answer is:
$$x = 0 \text{ and } x = 1$$
The value(s) of $x$ for which the determinant is zero are:
$$\boxed{x = 0 \text{ and } x = 1}$$