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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.
Definition of Rational Zeros Theorem. The rational zeros theorem (also called the rational root theorem) is used to check whether a polynomial has rational roots (zeros).It provides a list of all possible rational roots of the polynomial equation, where all coefficients are integers.If the equation has rational roots p / q, where p and q are integers, then p must divide evenly into the constant term a 0 and q must divide evenly into the leading coefficient an.In other words, p is a factor of Â± a 0 and q is a factor of Â± an.efinition of Rational Zeros Theorem. The rational zeros theorem (also called the rational root theorem) is used to check whether a polynomial has rational roots (zeros).