Mr. Jarrett on Algebraic Notation. "73 



26. The above symbol will be found extremely useful in 

 the theory of eliminations; but the following- examples may be 

 taken as specimens of a more general apjjlication. 



Ex. 1. Pr" {x + a^) = S„;'x'^-' . C/' -'"+'• "(«,). 



Ex. 2. If a, is the r'" root of the equation, o = 5„"+'«„_,a;"-', 

 then will a„,-i = C."-™+>-« (- a,). 



Ex. 3. To transform the equation o = 5',„" + 'fl„_,a'"'-', of which 

 the »■* root is a, into one of which the r"" root is ca,. 



The equation sought will be 



= ^J'^- 'x'"- ' . C;'-'"+ '• " ( - car) 



= ^„« + 'a;"'-' .c»-'" + '. 0/'-"'+ '"'(-«,) (Art. 24.) 



~ ^m "m— 1 • I- . J. . 



Ex. 4. If in the equation 

 we have 



then if a, is a root, «."' shall also be a root. 



For, = S,„"+'a„_^x'"-'^ 



= S„,"+^fl„_„^jX'"-', by hypothesis, 



and, dividing by P/' (— a,), 



= 5'„" + 'a;"-' . C/ -"•+'•" (-a,-') (Art. 25.), 



which is an equation of which the r* root is ar~^. 

 Vol. III. Part I. K 



