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Math Help - Graph of a polynomial function

  1. #1
    No one in Particular VonNemo19's Avatar
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    Graph of a polynomial function

    Describe, in your own words, that if the real zeros of a polynomial function occur in mutiplicity k, and k is even, then the graph touches (but does not touch) the x-axis at x = a, where x is a real zero of the given function.

    I'm having trouble here guys. Anything you could say on the matter would help. Thanks.

    Oh, by the way, when I say mutiplicity, I mean how many times x=a appears as a factor. E.G. in the polynomial x^2 + 2x + 1 = 0 , when factored we have (x + 1)(x + 1) = 0
    and the roots are x = -1 and x = -1 again so this
    has a root of even multiplicity and therefore the graph touches the x-axis but does not cross it at x = -1.

    Does anyone know what I'm talkin' about?!
    Last edited by VonNemo19; May 2nd 2009 at 02:40 PM. Reason: 1
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  2. #2
    Member pflo's Avatar
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    [quote=VonNemo19;309415]
    when I say mutiplicity, I mean how many times x=a appears as a factor. E.G. in the polynomial x^2 + 2x + 1 = 0 , when factored we have (x + 1)(x + 1) = 0 and the roots are x = -1 and x = -1 again so this has a root of even multiplicity and therefore the graph touches the x-axis but does not cross it at x = -1.
    [\quote]

    I know what you mean. It sounds to me like you just described what is going on in your own words....
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  3. #3
    No one in Particular VonNemo19's Avatar
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    No, I was clarifying what was meant by multiplicity, in case some were unfamiliar with the term, but able to describe what was happening to the graph.
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