# How do you solve x(x-3)^2>=0?

Dec 5, 2016

The answer is x in [0, +oo[

#### Explanation:

Let $f \left(x\right) = x {\left(x - 3\right)}^{2}$

The domain of $f \left(x\right)$ is ${D}_{f} \left(x\right) = \mathbb{R}$

and ${\left(x - 3\right)}^{2} \ge 0$, $\forall x \in \mathbb{R}$

So, the sign of $f \left(x\right)$ depends on the sign of $x$

Therefore, $f \left(x\right) \ge 0$, when x in [0, +oo[