Isn't this wrong? This worksheet
This question:
$$w^2 - w \leq 0$$
This answer:
$$(-\infty, -1] \cup [0, 1]$$
Isn't this wrong ? At $w = -2$, it becomes: $(-2)^2 - (-2)$, which is $4 + 2$, which is $\geq 0$. But might be that I must be wrong somewhere. Please correct me. Thanks.

In general, when you want to solve an inequality $p(x) \leq 0$ where $p$ is a polynomial, you first solve $p(x) = 0$ for the roots $x$ and then see if $p$ is positive or negative on each side of the roots. For $x^2 - x$, the roots are $x = 0,1$. It is then easy to check that $x^2 - x > 0$ when $x < 0$ or when $x > 1$, and $x^2 - x < 0$ when $0 < x < 1$. So the solution is just $0 \leq x \leq 1$.
