Posted by solomon on .
find the zeros and multiplicity of the equation, Range and interval q is positive.
q(x)=x^2(x+1)^2(x2)

algebra 
Steve,
since there are two double roots, the graph is tangent to the xaxis at 0 and 1. It crosses only at x=2.
So, since it is a 5th degree polynomial, with leading coefficient negative, it rises at the left end and falls on the right end.
So,
q > 0 for x < 1
q > 0 for 1 < x < 0
q > 0 for 0 < x < 2
q < 0 for x > 2
To confirm this, see the graph at
http://www.wolframalpha.com/input/?i=x^2%28x%2B1%29^2%28x2%29+for+1.5+%3C+x+%3C+2.1 
algebra 
solomon,
what are the zeros and multiplicity? and the Range of the equation?