# How do you solve x^4-13x^2+36<=0?

Oct 29, 2016

The answer is $- 3 \le x \le - 2$ and $2 \le x \le 3$

#### Explanation:

Let's start by factorising the expression
${x}^{4} - 13 {x}^{2} + 36 = \left({x}^{2} - 4\right) \left({x}^{2} - 9\right)$
$= \left(x - 2\right) \left(x + 2\right) \left(x - 3\right) \left(x + 3\right)$

So $\left(x - 2\right) \left(x + 2\right) \left(x - 3\right) \left(x + 3\right) \le 0$
Let's do a sign chart
$x$$\textcolor{w h i t e}{a a a a a a a a a a a}$$- 3$$\textcolor{w h i t e}{a a a a}$$- 2$$\textcolor{w h i t e}{a a a a}$$2$$\textcolor{w h i t e}{a a a a}$$3$
$x + 3$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a}$$+$
$x + 2$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a}$$+$
$x - 2$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a}$$+$
$x - 3$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a}$$+$