 | Arthur Schultze - Algebra - 1906 - 584 pages
...T7ie sum of the roots is equal to the coefficient of the second term with its sign changed. 2. The sum of the products of the roots taken two at a time is equal to the coefficient of the third term. B. The sum of the products of the roots taken three ai a time is equal to the coefficient of the fourth... | |
 | Charles Hamilton Ashton, Walter Randall Marsh - Algebra - 1907 - 304 pages
...coefficient of xn is unity the sum of the roots is equal to the negative of the coefficient of xn~l ; the sum of the roots taken two at a time is equal to the coefficient of xn~2; the sum «f the roots taken three at a time is equal to the negative of the coefficient of xn~8,... | |
 | William Charles Brenke - Algebra - 1910 - 374 pages
...so on. Exercise. Show by induction that the coefficient of the third highest power of x equals the sum of the products of the roots taken two at a time. 277. Fractional Roots. — An equation with integral coefficients, in which the coefficient of the... | |
 | Fletcher Durell - Algebra - 1915 - 426 pages
...sign changed equals the sum of the roots; (2) pz (or the coefficient of the third term) equals the sum of the products of the roots taken two at a time; (3) p3 (or the coefficient of the fourth term) with its sign changed equals the sum of the products... | |
 | William Charles Brenke - Algebra - 1917 - 212 pages
...so on. Exercise. Show by induction that the coefficient of the third highest power of x equals the sum of the products of the roots taken two at a time. 186. Fractional Roots. — An equation with integral coefficients, in which the coefficient of the... | |
 | John Wesley Young, Frank Millett Morgan - Functions - 1917 - 584 pages
...----- 1- rtrM + r2r3 H ----- hr^r.. (23) p3 = (24) A=( That is, — pt= Ae sum of the roots. p2 = the sum of the products of the roots taken two at a time. — pB = the sum of the products of the roots taken three at a time. (— !)"/>„ = the product of... | |
 | Leonard Eugene Dickson - Equations, Theory of - 1922 - 188 pages
...THEOREM. If ai, . . . , an arc the roots of equation (7), the sum of the roots is equal to -CI/CQ, the sum of the products of the roots taken two at a time is equal to C2/CQ, the sum of the products of the roots taken three at a time is equal to - CS/CQ, etc.; finally,... | |
 | Edward Ira Edgerton, Perry Amherst Carpenter - Algebra - 1925 - 398 pages
...The sum of the roots is equal to the coefficient of the second term with its sign changed. (2) The sum of the products of the roots taken two at a time...the coefficient of the third term. (3) The sum of tlw products of the roots taken three at a time is equal to the coefficient of tlw fourth term with... | |
 | Velma Elaine Massie - 1927 - 100 pages
...the four roots m, , mg, m„, and m. is equal to the negative of the coefficient P, of пц. S. The sum of the products of the roots taken two at a time is equal to the coefficient Pg of nig. 3. The sum of the products of the roots taken three at a time is equal to the negative of... | |
 | Ovid Wallace Eshbach, Byron D. Tapley - Technology & Engineering - 1990 - 2104 pages
...and a — bi. If n is odd, there is at least one real root. 4. The sum of the roots is -at/a0, the sum of the products of the roots taken two at a time is o2/a0, the sum of the products of the roots taken three at a time is -a3/t/0, and so on. The product... | |
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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. 
