Final answer:
The maximum number of roots for the polynomial given is 12, determined by the highest power of x in the polynomial, which is x to the 12th power.
Step-by-step explanation:
When asked to state the maximum number of roots for the polynomial f(x)=x7-4x5+3x2-9x12+4x-2x3, the answer can be found using the Fundamental Theorem of Algebra. This theorem states that the number of roots of a polynomial is equal to its highest degree when counted with multiplicity. In this case, the highest degree of the polynomial is 12, corresponding to the term -9x12. Therefore, the polynomial can have at most 12 roots.