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Numerical Solution of Nonlinear Equations of One Variable
Published in Azmy S. Ackleh, Edward James Allen, Ralph Baker Kearfott, Padmanabhan Seshaiyer, Classical and Modern Numerical Analysis, 2009
Azmy S. Ackleh, Edward James Allen, Ralph Baker Hearfott, Padmanabhan Seshaiyer
(Descartes’ rule of signs) Let p be a polynomial with real coefficients, letν1be the number of changes in the sign of the coefficients of p(x), and letν2be the number of changes in the sign of the coefficients of p(-x). Letk1and k2be the number of positive real roots and negative real roots of p(x). Thenk1≤ν1andν1−k1is even, k2≤ν2andν2−k2is even.
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
A useful Descartes rule of signs for the number of positive or negative real roots is available by observation for polynomials with real coefficients. The number of positive real roots is either equal to the number of sign changes, n, or is less than n by a positive even integer. The number of negative real roots is either equal to the number of sign changes, n, of P(-x), or is less than n by a positive even integer.
Numerical Methods
Published in William F. Ames, George Cain, Y.L. Tong, W. Glenn Steele, Hugh W. Coleman, Richard L. Kautz, Dan M. Frangopol, Paul Norton, Mathematics for Mechanical Engineers, 2022
A useful Descartes rule of signs for the number of positive or negative real roots is available by observation for polynomials with real coefficients. The number of positive real roots is either equal to the number of sign changes, n, or is less than n by a positive even integer. The number of negative real roots is either equal to the number of sign changes, n, of P(−x), or is less than n by a positive even integer.
A multi-echelon supply chain of deteriorating items with stock- and price-sensitive demand under consignment stock policy
Published in Engineering Optimization, 2023
M. Hemmati, S. M. T. Fatemi Ghomi, Mohsen S. Sajadieh
Considering the fact that , the roots of Equation (24) are equal to the roots of . Descartes’ rule of signs (Kelley 2008) is applied to obtain the number of real roots of .