How do you solve #(x-1)(x-2)(x-3)>=0# using a sign chart?

1 Answer
Jan 2, 2017

Answer:

The answer is # x in [1 ,2 ] uu [3, +oo [#

Explanation:

Let #f(x)=(x-1)(x-2)(x-3)#

Now, we can establish the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaaa)##1##color(white)(aaaaaa)##2##color(white)(aaaaaaa)##3##color(white)(aaaaaa)##-oo#

#color(white)(aaaa)##x-1##color(white)(aaaaa)##-##color(white)(aaaaa)##+##color(white)(aaaaa)##+##color(white)(aaaaa)##+#

#color(white)(aaaa)##x-2##color(white)(aaaaa)##-##color(white)(aaaaa)##-##color(white)(aaaaa)##+##color(white)(aaaaa)##+#

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

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

Therefore,

#f(x)>=0# when # x in [1 ,2 ] uu [3, +oo [#