The Universal Solution for Numerical and Literal Equations: By which the Roots of Equations of All Degrees Can be Expressed in Terms of Their CoefficientsMathematical book Company, 1899 - 195 páginas |
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The Universal Solution for Numerical and Literal Equations; by which the ... M. A. McGinnis Sin vista previa disponible - 2017 |
The Universal Solution for Numerical and Literal Equations; By Which the ... M. A. McGinnis Sin vista previa disponible - 2016 |
Términos y frases comunes
ab² absolute term ac² bc² biquadratic circular substitution coefficients contain two real contains imaginary roots cubic equation degree equations differences equa equation contains imaginary fifth find the roots formation of equation formula formula D fourth degree function given equation Horner method imaginary quantities lines or numbers minus quantity minus roots multiplying nx² obtain pair places of decimals pure imaginary quadratic factors ratics Real Imaginaries real quantities real root represent the roots root of unity roots in formation second term sign changed sign of absolute sixth degree solved square of sum square root squares of roots sum of diffs sum of roots sum of squares synthetic division Take the equation third degree third term three and three tion true sign unknown quantities values Whence write
Pasajes populares
Página 31 - The sum of the squares of the extremes of four numbers in arithmetical progression is 200, and the sum of the squares of the means is 136. What are the numbers ? Ans.
Página 20 - The sum of the products of the roots taken two and two, with their respective signs, is equal to the co-efficient of the third term.
Página 4 - This is no denial of the mathematical proposition that the whole is equal to the sum of all its parts...
Página 20 - The sum of the exponents of the two letters, in any term, is equal to the exponent of the given power. This last remark will enable us to verify any result obtained by the binomial theorem. Let us now apply these principles in the two following examples, in which the coefficients are omitted : — (a+6)6 . . . (a— l...
Página 20 - ... is equal to the sum of the products of the roots taken three and three ; and so on.
Página 20 - ... of all the roots with their signs changed. The coefficient of the third term is the sum of the products of all the roots, taken two and two.
Página 31 - How far will it fall in 16 seconds? 15. Find three quantities in arithmetical progression such that the sum of the squares of the first and third exceeds the second by 123, and the second exceeds one-third the first by 6.
Página 52 - ... positive roots, to include the first decimal place by Sturms' theorem. 2d. Then to find the decimal part of the first positive root, we arrange the co-efficients, and perform a succession of trans formations .by Synthetical Division, which must begin with the initial figures already known. We first transform the given equation into another whose roots shall be less by 1. The co-efficients of this new equation are, 1, 3, —4 and 1, and are all, except the first, marked by a star. The root of...
Página 11 - We have also shown that the sum of the squares of two lines is equal to the square of their difference plus twice their rectangle.
Página 153 - ... identical, and will not cease to exist if we replace in it these roots, the one by the other in any manner whatever. "Let us designate by y the first radical which enters into the value of...