Abstract
This chapter is devoted to the proof of some important relations between the coefficients of a polynomial and their complex roots; such results are generically known as the relations between roots and coefficients of a polynomial. We also discuss an important theorem of Newton on symmetric polynomials, which will reveal itself to be of central importance for the material of Chap. 20.
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Notes
- 1.
François Viète and Albert Girard , French mathematicians of the sixteenth and seventeenth centuries, respectively.
- 2.
Carl Gustav Jakob Jacobi , German mathematician of the nineteenth century.
References
A. Caminha, An Excursion Through Elementary Mathematics I - Real Numbers and Functions (Springer, New York, 2017)
A. Caminha, An Excursion Through Elementary Mathematics II - Euclidean Geometry (Springer, New York, 2018)
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Caminha Muniz Neto, A. (2018). Relations Between Roots and Coefficients. In: An Excursion through Elementary Mathematics, Volume III. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-77977-5_16
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DOI: https://doi.org/10.1007/978-3-319-77977-5_16
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