# How do you solve 4x^2-9x+2<0?

Nov 6, 2016

The answer is $\frac{1}{4} < x < 2$

#### Explanation:

Let's factorise the expression $f \left(x =\right) 4 {x}^{2} - 9 x + 2 = \left(4 x - 1\right) \left(x - 2\right)$
$\left(4 x - 1\right) \left(x - 2\right) < 0$
We make a sign chart to solve the problems
$\textcolor{w h i t e}{a a a a a a}$$x$$\textcolor{w h i t e}{a a a}$$- \infty$$\textcolor{w h i t e}{a a a}$$\frac{1}{4}$$\textcolor{w h i t e}{a a a}$$2$$\textcolor{w h i t e}{a a a}$$+ \infty$
$\textcolor{w h i t e}{a a a a}$$4 x - 1$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a}$$0$$\textcolor{w h i t e}{a}$$+$$\textcolor{w h i t e}{a a a}$$+$
$\textcolor{w h i t e}{a a a a a}$$x - 2$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a}$$-$$\textcolor{w h i t e}{a}$$0$$\textcolor{w h i t e}{a}$$+$
$\textcolor{w h i t e}{a a a a a}$$f \left(x\right)$$\textcolor{w h i t e}{a a a a a}$$+$$\textcolor{w h i t e}{a a a}$$-$$\textcolor{w h i t e}{a}$$0$$\textcolor{w h i t e}{a}$$+$

So $f \left(x < 0\right)$ when $\frac{1}{4} < x < 2$
graph{(4x-1)(x-2) [-7.024, 7.024, -3.51, 3.513]}