 | Isaac Todhunter - Equations, Theory of - 1861 - 330 pages
...45, if the equation be x" + plx"~l+pjc"~'+ ... = 0, we have —pl = the sum of the roots, pt = the sum of the products of the roots taken two at a time, and so on ; and it is manifest that the functions of the roots which occur here are symmetrical functions.... | |
 | Isaac Todhunter - Algebra - 1875 - 344 pages
...45, if the equation be x' +pix"~l + pox"~3 + ... = 0, we have — Pi = the sum of the roots, p3 = the sum of the products of the roots taken two at a time, and so on ; and it is manifest that the functions of the roots which occur here are symmetrical functions.... | |
 | Isaac Todhunter - Equations - 1882 - 348 pages
...45, if the equation be x" +plx"~1 +p^"~" + ... = 0, we have —P1 = the sum of the roots, p, = the sum of the products of the roots taken two at a time, and so on ; and it is manifest that the functions of the roots which occur here are symmetrical functions.... | |
 | James Morford Taylor - Algebra - 1889 - 340 pages
...= the sum of the roots ; p2 = the sum of the producís of the roots taken two at a time ; — pз = the sum of the products of the roots taken three at a time. (— l)" p„ = the product of the n roots, If a¡, я2, я„ ..., a„ denote the я roots of (A),... | |
 | James Morford Taylor - Algebra - 1889 - 400 pages
...— the sum of the roots ; p2 = the sum of the producís of the roots taken two at a time ; — p3 = the sum of the products of the roots taken three at a tijne. (— i)n pn = the product of the n roots. If а,, а2, ая, • •-, a„ denote the n roots... | |
 | Webster Wells - Algebra - 1889 - 584 pages
...term is equal to minus the sum of all the roots. The coefficient of the third term is equal to the sum of the products of the roots, taken two at a time. The coefficient of the fourth term is equal to minus the sum of the products of the roots, taken three... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1891 - 606 pages
...Equating coefficients of like powers of x in this identity, —p1 = S1 = sum of the roots; P2 = Sa= sum of the products of the roots taken two at a time; -pa = S3 =sum of the products of the roots taken three at a time ; (— l)"pn = Sa = product of the... | |
 | Arthur Latham Baker - Algebra - 1892 - 98 pages
...form o-"+/ i Jf"- i +/.,.v"- 2 +/ :i .v" J + A=°/j=Sum of the roots with their signs changed. / 2 =Sum of the products of the roots taken two at a time. */ n =Product of the n roots with their signs changed. (e) Imaginary roots occur in pairs. The last... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Plane trigonometry - 1893 - 434 pages
...(a;-a1)(a;-alt)(x-a3') (a:-an)=0, or #*-S1X*-1 + 82tf»-*-S!la?l-3+ + (-!)"£,, =0, where /Sj=sum of the roots; /S2 = sum of the products of the roots taken two at a time; £3=81100 of the products of the roots taken three at a time; Sn = product of the roots. [See Hall... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1895 - 508 pages
...-Pi=sv ( -!)-;>„= S„, in which S, stands for the sum of the roots a, b, c.,.k; S¡ stands for the sum of the products of the roots taken two at a time, and so on to SH, which equals the continued product of all the roots. That is : (1) The coefficient... | |
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The sum of the products of the roots taken two at a time is equal to the coefficient of the third term. 
