The trouble with Newton's method for finding the roots of a complex polynomial is knowing where to start the iteration. In this paper we apply the theory of rational maps and some estimates based on distortion theorems for univalent functions to find lower bounds, depending only on the degreed...
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Consider the equation x^2 - y^2 + z^2 - 2x + 2y + 4z + 1 = 0 . Reduce the equation to one of the standard forms. Classify the surface. Explain how to find restrictions in rational equations. Solve Cauchy-Euler. (a) x^2y" - xy' - 4y = 0 (b) x^2y" - 4xy' + 8y =...
Use the rational zero theorem to find all rational zeros of f(x) = 2x^4 - x^3 - 9x^2 + 4x + 4. Solve the equation using the rational root theorem and synthetic division. x^4 - 5x^2 - 24 = 0 How to use the rational root theorem. Using the rati...
How Constant Shifts Affect the Zeros of Certain Rational Harmonic Functionsdoi:10.1007/S40315-018-0240-8Jrg LiesenJan ZurSpringer Berlin HeidelbergJ. Liesen and J. Zur, How constant shifts affect the zeros of certain rational har- monic functions, Comput. Methods Funct. Theory, 18 (2018), pp...
However, problems related to how mathematicians find problems, pose problems, think about problems, and solve problems in mathematical science have rarely been touched upon until now. Therefore, “Where do good problems come from?” [6]. The motivation of the current paper is to start an ...
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