# How do you solve 2x^2+5x-12>0 using a sign chart?

Dec 1, 2016

The answer is x in] -oo,-4 [ uu ] 3/2, oo[

#### Explanation:

Let's start by solving the quadratic equation

$a {x}^{2} + b x + c = 0$

Our equation is $f \left(x\right) = 2 {x}^{2} + 5 x - 12$

Let's calculate the discriminant

$\Delta = {b}^{2} - 4 a c = 25 - 4 \cdot 2 \left(- 12\right) = 121$

$x = \frac{- b \pm \sqrt{\Delta}}{2 a}$

$x = \frac{- 5 \pm \sqrt{121}}{4}$

$x = \frac{- 5 \pm 11}{4}$

${x}_{1} = - \frac{16}{4} = - 4$

${x}_{2} = \frac{6}{4} = \frac{3}{2}$

Let's do our 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}$$- 4$$\textcolor{w h i t e}{a a a a}$$\frac{3}{2}$$\textcolor{w h i t e}{a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$x + 4$$\textcolor{w h i t e}{a a a a a}$$-$$\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}$$x - \frac{3}{2}$$\textcolor{w h i t e}{a a a a}$$-$$\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}$$f \left(x\right)$$\textcolor{w h i t e}{a a a a a a}$$+$$\textcolor{w h i t e}{a a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$

So, $f \left(x\right) > 0$, when x in] -oo,-4 [ uu ] 3/2, oo[