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poly-roots.pdf

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Roots of Random Polynomials Tamique de Brito, Tony Wang, Yang Yan November 2019 1 Introduction The roots of polynomials are interesting mathematical objects. The fundamental theorem of algebra says that given a0 , . . . , an ∈ C, there exist r1 , . . . , rn ∈ C unique up to permutation such that a0 + a1 z + · · · + an−1 z n−1 + z n = (z − r1 )(z − r2 ) · · · (z − rn ). In other words, the roots of a complex polynomial are uniquely determined by its coefficients. While it is easy to find the coefficients of a…

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