Number of integral roots of $|\mathrm{x}-1|\left|{\mathrm{x}}^2-2\right|=2$ is

We have $|\mathrm{x}-1|\left|{\mathrm{x}}^2-2\right|=2$

Since x is an integer, we have

$|\mathrm{x}-1|=1\text{ and }\left|{\mathrm{x}}^2-2\right|=2$

or $|\mathrm{x}-1|=2\text{ and }\left|{\mathrm{x}}^2-2\right|=1$

$\therefore \mathrm{x}=0,2 \mathrm{and} \mathrm{x}=0,\pm 2$

or $\mathrm{x}=-1,3\text{ and }\mathrm{x}=\pm 1$

Therefore, solutions are -1, 0,2