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"?
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