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algebra

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find the zeros and multiplicity of the equation, Range and interval q is positive.
q(x)=-x^2(x+1)^2(x-2)

  • algebra - ,

    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

  • algebra - ,

    what are the zeros and multiplicity? and the Range of the equation?

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