Thread: 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?!

[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....

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.