How do you solve #9-x^2<0# using a sign chart?

1 Answer
Dec 21, 2016

Answer:

The answer is #x in ] -oo,-3 [ uu ] 3, oo[ #

Explanation:

Let #f(x)=9-x^2=(3-x)(3+x)#

Now we can do the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-3##color(white)(aaaa)##3##color(white)(aaaa)##+oo#

#color(white)(aaaa)##3+x##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##3-x##color(white)(aaaaa)##+##color(white)(aaaa)##+##color(white)(aaaa)##-#

#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##-#

Therefore,

#f(x)<0#, when # x in ] -oo,-3 [ uu ] 3, oo[ #