Researches respecting the imaginary roots of numerical equations
Subtitle: being a continuation of Newton's investigations on that subject, and forming an appendix ... of the higher orders." By J. R. Young.
Publisher: Scholarly Publishing Office, University of Michigan Library
Published: December 20, 2005
Language: eng
Format: Paperback
Number of pages: 63
ISBN-13: 9781418178154
Subjects: Mathematics / General
First sentence: (1.) IT has already been shown (page 323) that if the general equation Anxn + An-1xn-1 + An-2xn-2 + .... A2x2 + A1x + A0 = 0....[1] be transformed into another, by substituting x + r for x, and then r be so determined that the second coefficient of the transformed equation may vanish, the third coefficient must be An-2/An - n(n-1)/2 {An-1/nAn}2 Consequently if, when this evanescence takes place, the expression here written be positive-like the leading coefficient An,- the zero, then occurring between like signs in the transformed, will indicate the existence of a pair of imaginary roots in the original equation.