Not sure if anyone can understand the title (my math vocab/basics are lacking), but basically this:
Given a specific function that has a certain number of a specific set of zeros, I want to be able to find another function that has all of the same zeros, but with another zero added to the function.
An example would be something like, given a function with the roots 1 and 3, say I wanted to find another function with the same roots but with the added root 22. Also, would this be possible backwards? If I have a function with the roots 1,3,22, would I be able to find one with roots 1 and 3 using the previous function?
How costly would this be from a time complexity stance?
Thanks!