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[ #