 | Algebra - 1995 - 92 pages
...third degree it is possible to write it as: x3 + bix2 + bjx + bj = 0 where -bi = sum of the roots bj = sum of the products of the roots taken two at a time. (-1)*Ь3 = product of the roots. C) It is possible to determine the roots of an equation by writing... | |
 | Ross Honsberger - Mathematics - 1997 - 332 pages
...sum of the roots = 4a = 4, and a = 1, and the roots are 1 - 3d, 1 - d, 1 + d, and 1 + 3d. Also the sum of the products of the roots taken two at a time is (1 - 4d + 3d2) + (1 - 2d - 3d2) + (1 - 9d2) + (1 - d2) + (1 + 2d - 3d2) + (1 + 4d + 3d2) = -14, giving... | |
 | N. P. Bali, N. Ch. Narayana Iyengar - Engineering mathematics - 2004 - 1438 pages
...where Za, = sum of all roots. Zoc^ = sum of the products of roots taken two at a time. £0)020(3 = sum of the products of the roots taken three at a time and so on. Equating die co-efficients of like powers of x on both sides of (/), we have -aoZa,=a, A... | |
 | J.B. Dixit - C (Computer program language) - 2005 - 432 pages
...an] ...(i) where Zo<1 = sum of all roots. loc^ = sum of the products of roots taken two at a time. = sum of the products of the roots taken three at a time and so on. h un 0 a. 1 bJ1 _ "2 ' 1 . . n-! ...6 „A a n-2 ei n n-! bn 0 b, 1 60 "2 b , nl R Equating... | |
 | J.B. Dixit - C (Computer program language) - 2006 - 684 pages
...l)n cila2a3 aj where Zcti = sum of all roots. = sum of the products of roots taken two at a time. = sum of the products of the roots taken three at a time and so on. Equating the co-efficients of like powers of x on both sides of (i), we have a0 a0 I0 a0... | |
 | Aeronautics - 1962 - 782 pages
...and /] u2 = - -\ l .. + J] -2 , we have this condition on the po' d(k+i) •- ' (k+j) 1 eigenvalues. The sum of the products of the roots taken three at a time is + »j>m (k+m)(k+j)(k+p) 8d* <r> (j+k) (j+k+1) (j+k+2) «ond summation having the value •* ^ when... | |
 | Society of Automotive Engineers - Aeronautics - 1928 - 1082 pages
...which the negative of the coefficient of t' is the sum of the roots and the coefficient of t is the sum of the products of the roots taken two at a time. Denoting the unknown roots by £, and t,, we get ', + '*— V (2E)/p = Q Ma— tV (2E)/p—t,\I (2E)/p... | |
 | Royal Society (Great Britain) - Electronic journals - 1919 - 658 pages
...before, the sum of the roots <&j + <I>2 + . . . + 4>B is equal to a! + fta + . . . + /' „. Also the sum of the products of the roots taken two at a time = («!&») + (aiC3)+... kk But 4>» = ^rj, and hn = — - as before. Also (ai&a) is the product of... | |
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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. 
