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For the sake of simplicity, in the sequel a (Laurent) polynomial of negative degree is understood to be the zero polynomial and, similarly, a banded matrix with negative bandwidth reduces to the zero matrix.
We say that is a root or zero of a polynomial, , if. In other words, is a root or zero of a polynomial if it is a solution to the equation. In the next couple of sections we will need to find all the zeroes for a given polynomial. So, before we get into that we need to get some ideas out of the way regarding zeroes of polynomials that will help us in that process.