Adv Pre-Calc - 2-3 Real Zeros of Polynomial Functions
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Divide using long division.
منابع مشابه
A Few Riddles Behind Rolle's Theorem
First year undergraduates usually learn about classical Rolle’s theorem saying that between two consecutive zeros of a smooth univariate function f one can always find at least one zero of its derivative f . In this paper we study a generalization of Rolle’s theorem dealing with zeros of higher derivatives of smooth univariate functions enjoying a natural additional property. Namely, we call a ...
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We prove a complex analytic analog of the classical Rolle theorem asserting that the number of zeros of a real smooth function can exceed that of its derivative at most by 1. This result is used then to obtain upper bounds for the number of complex isolated zeros of: (1) functions deened by linear ordinary diierential equations (in terms of the magnitude of the coeecients of the equations); (2)...
متن کاملLINEAR ESTIMATE OF THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR A KIND OF QUINTIC HAMILTONIANS
We consider the number of zeros of the integral $I(h) = oint_{Gamma_h} omega$ of real polynomial form $omega$ of degree not greater than $n$ over a family of vanishing cycles on curves $Gamma_h:$ $y^2+3x^2-x^6=h$, where the integral is considered as a function of the parameter $h$. We prove that the number of zeros of $I(h)$, for $0 < h < 2$, is bounded above by $2[frac{n-1}{2}]+1$.
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تاریخ انتشار 2010