Question:

Find a polynomial f(x) of degree 6 such that 0,3 are zeroes of multiplicity 3 and f(2) = -24.

Can someone explain this step-by-step? what exactly is "multiplicity"?

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- Nov 25th 2008, 09:07 AMmwokFinding a polynomial with degree, zeroes, and multiplicity
Question:

Find a polynomial f(x) of degree 6 such that 0,3 are zeroes of multiplicity 3 and f(2) = -24.

Can someone explain this step-by-step? what exactly is "multiplicity"? - Nov 25th 2008, 09:12 AMMoo
- Nov 25th 2008, 09:20 AMmwok
I see.

How about if it was:

Find a polynomial f(x) of degree 5 such that 0,3 are zeroes of multiplicity 3 and f(2) = -24. (Notice the degree is now 5)

How would you solve this one? - Nov 25th 2008, 09:27 AMMoo
It is not possible.

Note that if the degree of a polynomial is n, there are**at most**5 roots for it.

If a root**a**has a multiplicity of b, it's like you have b roots that are all equal to**a**.

In fact, if**a**has a multiplicity of b, you have $\displaystyle f(a)=f'(a)=f''(a)=\ldots=f^{(b-1)}(a)=0$

$\displaystyle f^{(b-1)}(x)$ denots the (b-1)th derivative of f.

I replied to someone here : http://www.mathhelpforum.com/math-he...tiplicity.html dunno if it can give you another view on it