# How do you solve x^4(x-2)>=0 using a sign chart?

Dec 30, 2016

The answer is x in [2, +oo[

#### Explanation:

Let $f \left(x\right) = {x}^{4} \left(x - 2\right)$

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

$\forall x \in \mathbb{R} , {x}^{4} \ge 0$

The sign chart is very simple

$\textcolor{w h i t e}{a a a a}$$x$$\textcolor{w h i t e}{a a a a a a}$$- \infty$$\textcolor{w h i t e}{a a a a a a}$$2$$\textcolor{w h i t e}{a a a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$x - 2$$\textcolor{w h i t e}{a a a a a a a}$$-$$\textcolor{w h i t e}{a a a a a a a}$$+$

$\textcolor{w h i t e}{a a a a}$$f \left(x\right)$$\textcolor{w h i t e}{a a a a a a a a}$$-$$\textcolor{w h i t e}{a a a a a a a}$$+$

Therefore,

$f \left(x\right) \ge 0$, when  x in [2, +oo[