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HandWiki. Properties of Polynomial Roots. Encyclopedia. Available online: https://encyclopedia.pub/entry/35421 (accessed on 22 September 2026).
HandWiki. Properties of Polynomial Roots. Encyclopedia. Available at: https://encyclopedia.pub/entry/35421. Accessed September 22, 2026.
HandWiki. "Properties of Polynomial Roots" Encyclopedia, https://encyclopedia.pub/entry/35421 (accessed September 22, 2026).
HandWiki. (2022, November 21). Properties of Polynomial Roots. In Encyclopedia. https://encyclopedia.pub/entry/35421
HandWiki. "Properties of Polynomial Roots." Encyclopedia. Web. 21 November, 2022.
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In mathematics, a univariate polynomial is an expression of the form where the ai belong to some field, which, in this article, is always the field [math]\displaystyle{ \mathbb C }[/math] of the complex numbers. The natural number n is known as the degree of the polynomial. In the following, p will be used to represent the polynomial, so we have A root of the polynomial p is a solution of the equation p = 0: that is, a complex number a such that p(a) = 0. The fundamental theorem of algebra combined with the factor theorem states that the polynomial p has n roots in the complex plane, if they are counted with their multiplicities. This article concerns various properties of the roots of p, including their location in the complex plane.
natural number
complex number
multiplicities
References
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