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Published byNathaniel Jackson Modified over 6 years ago

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Section 4.3 Zeros of Polynomials

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Approximate the Zeros

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Fundamental Theorem of Algebra If a polynomial f(x) has positive degree and complex coefficients, then f(x) has at least one complex zero.

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Descartes’ Rule of Signs Let f(x) be a polynomial with real coefficients and a nonzero constant term. The number of positive real zeros of f(x) either is equal to the number of variations of sign in f(x) or is less than that number by an even integer The number of negative real zeros of f(x) either is equal to the number of variations of sign in f(-x) or is less than that number by an even integer.

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Rational Root Theorem If the polynomial has integer coefficients and if c/d is a rational zero of f(x) such that c and d have no common prime factor, then: The numerator, c, of the zero is a factor of the constant term a 0 The denominator, d, of the zero is a factor of the leading coefficient a n.

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