Abstract
In this lecture, we shall prove the Fundamental Theorem of Algebra, which states that every nonconstant polynomial with complex coefficients has at least one zero. Then, as a consequence of this theorem, we shall establish that every polynomial of degree n has exactly n zeros, counting multiplicities. For a given polynomial, we shall also provide some bounds on its zeros in terms of the coefficients.
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© 2011 Springer Science+Business Media, LLC
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Agarwal, R.P., Perera, K., Pinelas, S. (2011). The Fundamental Theorem of Algebra. In: An Introduction to Complex Analysis. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-0195-7_19
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DOI: https://doi.org/10.1007/978-1-4614-0195-7_19
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Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-0194-0
Online ISBN: 978-1-4614-0195-7
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