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I want the all the properties of Chapter - Polynomials
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properties of polynomial roots may be deduced from the coefficients of the polynomial, without having to compute the polynomial explicitly.
More precisely, given an univariate polynomialwith real or complex coefficients
{\displaystyle p(x)=a_{0}+a_{1}x+\cdots +a_{n}x^{n},}
with {\displaystyle a_{n}\neq 0}, a root of p is a complex number α such that p(α) = 0.
The fundamental theorem of algebracombined with the factor theorem states that the polynomial p has n roots, if they are counted with their multiplicities.
More precisely, given an univariate polynomialwith real or complex coefficients
{\displaystyle p(x)=a_{0}+a_{1}x+\cdots +a_{n}x^{n},}
with {\displaystyle a_{n}\neq 0}, a root of p is a complex number α such that p(α) = 0.
The fundamental theorem of algebracombined with the factor theorem states that the polynomial p has n roots, if they are counted with their multiplicities.
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