How do you solve #x^2-2x-5<=0# using a sign chart?

1 Answer
Oct 30, 2016

Answer:

The answer is #1-sqrt6<=x<=1+sqrt6#

Explanation:

First we start by solving #y=x^2-2x-5=0#
We calculate #Delta=b^2-4ac=4+20=24#

So the roots are #=(2+-sqrt24)/2=(2+-2sqrt6)/2#
so the roots are #1+sqrt6# and #1-sqrt6#
We can do the sign chart

#x##color(white)(aaaaaa)##-oo##color(white)(aaa)##1-sqrt6##color(white)(aaa)##1+sqrt6##color(white)(aaa)##+oo#
#1-sqrt6##color(white)(aaaa)##-##color(white)(aaa)##0##color(white)(aaaa)##+##color(white)(aaaaa)##+#
#1+sqrt6##color(white)(aaaa)##-##color(white)(aaa)####color(white)(aaaaa)##-##color(white)(aaaaa)##+#
#y##color(white)(aaaaaaaaa)##+##color(white)(aaaaaaaa)##-##color(white)(aaaaa)##+##color(white)(aaaaa)#

So #x^2-2x-5<=0# when #1-sqrt6<=x<=1+sqrt6#