# How do you solve 4x^2-8x>=0 using a sign chart?

Jan 25, 2017

The answer is x in ]-oo, 0] uu [2, +oo [

#### Explanation:

Let s factorise the expression

$4 {x}^{2} - 8 x = 4 x \left(x - 2\right)$

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

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

Now we can build the sign chart

$\textcolor{w h i t e}{a a a a}$$x$$\textcolor{w h i t e}{a a a a}$$- \infty$$\textcolor{w h i t e}{a a a a a}$$0$$\textcolor{w h i t e}{a a a a a}$$2$$\textcolor{w h i t e}{a a a a}$$+ \infty$

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

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

Therefore,

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