posted by solomon .
find the zeros and multiplicity of the equation, Range and interval q is positive.
since there are two double roots, the graph is tangent to the x-axis 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.
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
what are the zeros and multiplicity? and the Range of the equation?