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

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Answer 1 · 2016-12-20T15:36:00

You can factorize into $3w^2(w^2-9)>0$

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

Which leaves us with $w^2-9>0->w^2>9$

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

Answer 2 · 2016-12-20T15:50:53

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

Let $f(w)=3w^4-27w^2$

$=3w^2(w+3)(w-3)$

$w^2 >0, AA win RR$

Let's do a sign chart

$color(white)(aaaa)$ $w$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-3$ $color(white)(aaaa)$ $3$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $w+3$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $w-3$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $f(w)$ $color(white)(aaaaaa)$ $+$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $+$

Therefore,

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

How do you solve 3w^4-27w^2>03w^4-27w^2>0 using a sign chart?