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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.
Zero is an acceptable value for a variable. As a general rule, if you solve an equation and get x equals zero, that's just what it is: zero. There is one solution. Example: 10x +1 = 5x +1. 5x = 1 - 1. 5x = 0. x = 0. There is one solution, zero. If you solve for x and get two solutions, such as 2 and 0, there are two answers.