| Charles Bossut - Astronomy - 1803 - 540 pages
...third is the sum of the products of the roots taken two fcy two: that the coefficient of the fourth is **the sum of the products of the roots taken three by three** with contrary signs ; and so on, to the last term, which is the product of all the roots taken with... | |
| John Hind - Algebra - 1837 - 539 pages
...q = 0, is manifestly equivalent to a; 2 - (a +/3) # + 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. COK. 3. Since a? 2 - (a + /3) a? + a/3 =... | |
| Isaac Todhunter - Equations, Theory of - 1861 - 279 pages
...coefficient of the third term is equal to the sum of the products of every two of the roots ; the coefficient **of the fourth term with its sign changed is equal to the sum of the** products of every three of the roots ; and so on. Thus generally if p r denote as usual the coefficient... | |
| Thomas Kimber - Mathematics - 1865 - 192 pages
...0, Or x* — (a + ft) x + a 0 = 0. 6 and id 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*" + p x" =... | |
| CHARLES DAVIES, LL.D. - 1871
...is equal to the sum of the different products of the roots, taken two in a set. 3d. The co-efficient **of the fourth term, with its sign changed, is equal to the sum of the** different products of the roots, taken three in a set, and so on. 4th. The absolute term, with its... | |
| Joseph Ficklin - Algebra - 1874 - 418 pages
...of the roots, taken two and tioo; 2 4 1—1 + 2 I +1 + 4 — 2 — 2 + 4 — 8 3. Tlie coefficient **of the fourth term with its sign changed is equal to the sum of the products of the** roots,taken three and three; and so on. 4. If the degree of the equation is even, the absolute term... | |
| 1874
...) (x - p) = 0, Or x* — (a + /?) x + a $ = 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. 188. Every equation of the form, x*™ + px m... | |
| Isaac Todhunter - Equations, Theory of - 1880 - 328 pages
...coefficient of the third term is equal to the sum of the products of every two of the roots; the coefficient **of the fourth term with its sign changed is equal to the sum of the** products of every three of the roots; and so on. Thus generally if p r denote as usual the coefficient... | |
| WILLIAM SNOW BURNSIDE, M.A - 1881
...the third term is equal to the mm of the products of the roots taken two by two. The coefficient p^ **of the fourth term with its sign changed is equal...alternately negative and positive, and the number of roots** multiplied to g ether in each term of the corresponding function of the roots increasing by unity,... | |
| William Snow Burnside, Arthur William Panton - Determinants - 1881 - 387 pages
...the third term is equal to the sum of the products of the roots taken two by two. The coefficient p **3 of the fourth term with its sign changed is equal...coefficients being taken alternately negative and** posit ii'c, and the number of roots muffipfifd together in each term of the corresponding function... | |
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