Let $L$ be the following language.
$L=\left\{P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \mid P\right.$ is a polynomial with an integral root $\}$.
Explain why the following Turing Machine description cannot decide the language $L$.
$\text{Description of M}:$ The input is a polynomial $P$ over the variables $x_{1}, \ldots, x_{n}$.
- Try all possible settings of $x_{1}, \ldots, x_{n}$ to integer values.
- Evaluate the polynomial on all values.
- If any of these settings evaluate to $0,$ accept. Else, reject.