# How do you solve 3w^4-27w^2>0 using a sign chart?

Dec 20, 2016

You can factorize into $3 {w}^{2} \left({w}^{2} - 9\right) > 0$

#### Explanation:

Since $3 {w}^{2} \ge 0$ you may divide by it without changing the $>$sign.
If $w = 0$ it won't fit the bill, so $w \ne 0$

Which leaves us with ${w}^{2} - 9 > 0 \to {w}^{2} > 9$

So either $w < - 3 \mathmr{and} w > + 3$
graph{3x^4-27x^2 [-16.04, 16, -8.03, 8]}

Dec 20, 2016

The answer is w in ] -oo,-3 [ uu ] 3,+ oo[

#### Explanation:

Let $f \left(w\right) = 3 {w}^{4} - 27 {w}^{2}$

$= 3 {w}^{2} \left(w + 3\right) \left(w - 3\right)$

${w}^{2} > 0 , \forall w \in \mathbb{R}$

Let's do a sign chart

$\textcolor{w h i t e}{a a a a}$$w$$\textcolor{w h i t e}{a a a a}$$- \infty$$\textcolor{w h i t e}{a a a a}$$- 3$$\textcolor{w h i t e}{a a a a}$$3$$\textcolor{w h i t e}{a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$w + 3$$\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}$$w - 3$$\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}$$f \left(w\right)$$\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,

$f \left(w\right) > 0$, when w in ] -oo,-3 [ uu ] 3,+ oo[