How do you solve #2x^3+x^2>6x# using a sign chart?

1 Answer
Narad T.
Oct 18, 2016

the answer is #-2< x< 0# and #x>3/2#

Explanation:

We need to factorise the expresson
#2x^3+x^2-6x>0 =>x(2x^2+x-6)>0#
#=># #x(2x-3)(x+2)>0#
So the key points we have to look at are #x=0# #x=3/2# and #x=-2#

If #x<-2# the expression is#<0#
If #-2< x< 0# the expression is #>0#
If #0< x< 3/2# the expression is #<0#
If #x>3/2# the expression is #>0#
So the answer is #-2< x< 0# and #x>3/2#

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