How do you solve #x^4-13x^2+36<=0#?

1 Answer
Oct 29, 2016

Answer:

The answer is #-3<=x<=-2# and #2<=x<=3#

Explanation:

Let's start by factorising the expression
#x^4-13x^2+36=(x^2-4)(x^2-9)#
#=(x-2)(x+2)(x-3)(x+3)#

So #(x-2)(x+2)(x-3)(x+3)<=0#
Let's do a sign chart
#x##color(white)(aaaaaaaaaaa)##-3##color(white)(aaaa)##-2##color(white)(aaaa)##2##color(white)(aaaa)##3#
#x+3##color(white)(aaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+##color(white)(aaaa)##+##color(white)(aaa)##+#
#x+2##color(white)(aaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+##color(white)(aaa)##+#
#x-2##color(white)(aaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+##color(white)(aaa)##+#
#x-3##color(white)(aaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##-##color(white)(aaa)##+#