 In every algebraic equation, the coefficient of whose highest term is unity, the coefficient pi of the second term with its sign changed is equal to the sum of the roots. The coefficient...  A College Algebra - Page 427by Henry Burchard Fine - 1904 - 595 pagesFull view - About this book
 | John Hind - Algebra - 1837 - 584 pages
...a?2 - pas + q = 0, is manifestly equivalent to a?8 - (a + )8) a? + a/3 = 0 : where the coefficient of the second term, with its sign changed, is equal to the sum of the roots, and the third term is equal to their product. 144. Con. 3. Since a? — (a + ft) tv + a/3... | |
 | Joseph B. Mott - Algebra - 1855 - 58 pages
...af+AVl~1+BVi-2+CVl-3+&;c. to (last coefficient) xn~n = 0, is such, 1°, that the coefficient of the second term (A'), with its sign changed, is equal to the sum of all the roots. 2° That the coefficient of the third term (B') is equal to the sum of all the products that can be... | |
 | Isaac Newton - Curves, Algebraic - 1860 - 177 pages
...let ^—(aa: + b)yn~1 + (ca;* + da: + e)yn~*'-' &c. = o Then, since in every equation the coefficient of the second term with its sign changed is equal to the excess by which the sum of the positive exceeds the sum of the negative roots, where this term is deficient,... | |
 | Charles Davies - Algebra - 1860 - 412 pages
...the following conclusions with reference to the values of the co-efficients : 1st. The co-efficient of the second term, with its sign changed, is equal to the algebraic sum of the roots of the equation. 2d. The co-efficient of the third term is equal to the... | |
 | Isaac Todhunter - Equations, Theory of - 1861 - 330 pages
...product of all the roots with their signs changed. Or we may enunciate the laws thus : the coefficient of the second term with its sign changed is equal to the sum of the roots ; the coefficient of the third term is equal to the sum of the products of every two of the... | |
 | Thomas Kimber - Mathematics - 1865 - 302 pages
...0, (х - a) (,r - /8) = 0, Or я* — (a + /3) x + a ß = 0. Whence it appears that the coefficient of the second term, with its sign changed, is equal to the sum of the roots, and the third term is equal to their product. 183. Every equation of the form, x'm + p xm... | |
 | Charles Davies - Algebra - 1871 - 404 pages
...the following conclusions with reference to the values of the co-efficients : 1st. The co-efficient of the second term, with its sign changed, is equal to the algebraic sum of the roots of the equation. 2d. The co-efficient of the third term is equal to the... | |
 | Isaac Todhunter - Algebra - 1875 - 344 pages
...product of all the roots with their signs changed. Or we may enunciate the laws thus : the coefficient of the second term with its sign changed is equal to the sum of the roots ; the coefficient of the third term is equal to the sum of the products of every two of the... | |
 | William Snow Burnside, Arthur William Panton - Determinants - 1886 - 474 pages
...— In every algebraic equation, the coefficient of whose highest term is unity, the coefficient pi of the second term with its sign changed is equal to the sum of the roots. The coefficient p, of the third term is equal to the sum of the products of the roots taken... | |
 | William Snow Burnside, Arthur William Panton - Determinants - 1886 - 480 pages
...— In every algebraic equation, the coefficient oj trhose highest term is unity, the coefficient pi of the second term with its sign changed is equal to the sum of the roots. The coefficient p2 of the third term is equal to the sum of the products of the roots taken... | |
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