One of the subjects which I had visited in my past, was to write a C++ program that approximates the roots of polynomials, but that needed to deal with ‘Doubled Roots’ in a special way, just because the search algorithm within that program, which searches for the roots, cannot deal with doubled roots. And what I found was, roots cannot only be doubled, but can have multiplicities higher than (2). After not having pondered that programming project from the past, for some time, I now come back to rethink it, and find that it can be given a lecture of sorts, all to itself.
So, this is a link to a work-sheet, in which I try to explain Roots with Multiplicities, maybe to people with limited knowledge in Calculus:
And as those two documents mention, the following is a link to the earlier blog posting, from which readers can download the C++ program, as well as to find instructions on how to compile it, on Linux computers:
Hence, the C++ program linked to in the earlier blog posting, needed to make use of the subject, that the two PDF Files describe.
(Updated 4/25/2019, 7h15 … )