 | Charles Brooke - 1829 - 386 sider
...divided by 1, «г, т", &с. the roots will all be divided by m. To transform the equation ф (.«) = 0 into one whose roots are the reciprocals of the roots of the former : assume л? = - , У we obtain aaaa ( W. 280— 97; Bour. 275— 80 ; G. 310— 25.) To take... | |
 | Charles William Hackley - 1846 - 544 sider
...0 has a real root between 0 and -. D 287. To find an inferior limit of the positive roots, we must transform the equation into one whose roots are the reciprocals of the roots of the former : and the reciprocal of the superior limit of the roots of the transformed equation, found by... | |
 | Isaac Todhunter - 1861 - 330 sider
...the positive roots of the equation /(a;) = 0. any of the positive roots. For transform the proposed equation into one whose roots are the reciprocals of the roots of the proposed equation, and then the reciprocal of the superior limit of the positive roots of the transformed... | |
 | Charles William Hackley - 1864 - 532 sider
...root between 0 and -. D 287. To find an inferior limit of the positive roots, we must transfora tU equation into one whose roots are the reciprocals of the roots of die froi i' and the reciprocal of the superior limit of the roots of the transformed «f» tion. found... | |
 | Isaac Todhunter - 1875 - 344 sider
...equation, that is a number which is not greater than any of the positive roots. For transform the proposed equation into one whose roots are the reciprocals of the roots of the proposed equation, and then the reciprocal of the superior limit of the positive roots of the transformed... | |
 | William Snow Burnside, Arthur William Panton - 1881 - 407 sider
...#+770=0, 5. Remove the fractional coefficients from the equation 32. Reciprocal Roots.-—To transform an equation into one whose roots are the reciprocals of the roots of the proposed equation, we change x into - in the identity of Art. 30. This gives, after certain easy reductions,... | |
 | Isaac Todhunter - 1882 - 348 sider
...equation, that is a number which is not greater than any of the positive roots. For transform the proposed equation into one whose roots are the reciprocals of the roots of the proposed equation, and then the reciprocal of the superior limit of the positive roots of the transformed... | |
 | Leonard Marshall - 1883 - 184 sider
...c ... if those of x are а, 6, c ... ie the signs of all the roots are changed. 8. To transform an equation into one whose roots are the reciprocals of the roots of the original equation. Put y = — , thenx= — , and equation (i.) becomes x у К7)n+*(?Г1+*(?Г1;"... | |
 | William Snow Burnside, Arthur William Panton - 1886 - 480 sider
...Am. x1 - 25.T5 + 375Z5- 11700 = 0. 32. Reciprocal Roots and Reciprocal Equations. — To transform an equation into one whose roots are the reciprocals of the roots of the proposed equation, we change x into - in the if identity of Art. 30. This substitution gives, after... | |
 | William Snow Burnside, Arthur William Panton - 1886 - 474 sider
...Am. x* - 25^ + 375Z2- 11700 = 0. 32. Reciprocal Roots and Reciprocal Equations. — To transform an equation into one whose roots are the reciprocals of the roots of the proposed equation, we change x into - in the identity of Art. 30. This substitution gives, after certain... | |
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For transform the proposed equation into one whose roots are the reciprocals of the roots of the proposed equation... 
