Asked by solomon
find the zeros and multiplicity of the equation, Range and interval q is positive.
q(x)=-x^2(x+1)^2(x-2)
q(x)=-x^2(x+1)^2(x-2)
Answers
Answered by
Steve
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.
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%28x-2%29+for+-1.5+%3C+x+%3C+2.1
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%28x-2%29+for+-1.5+%3C+x+%3C+2.1
Answered by
solomon
what are the zeros and multiplicity? and the Range of the equation?
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