...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...

...root between 0 and -. 6 287. 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 tho superior limit of the roots of the transformed equation, found by...

...the proposed equation, multiplying by y°, and reversing the order of the terms, we have the equation whose roots are the reciprocals of the roots of the proposed equation. The transformation is then effected by simply changing the order of the coefficients of the given equation....

...root between 0 and -• . 6 46. 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 proposed equation ; and the reciprocal of the superior limit of the roots of the transformed equation, found by the preceding...

...proposed cquaу у tion, multiplying by y", and reversing the order of the terms, we have the equation whose roots are the reciprocals of the roots of the proposed equation. Cor. 1. Hence an equation may be transformed into another whose roots shall be greater or less than...

...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...

...an inferior limit of the positive roots of an equation, that is a number which is not greater than any of the positive roots. For transform the proposed...equation. Thus suppose the proposed equation to be put - for x, and multiply by y" and divide by pn, so that the (/ transformed equation is P. JP. PP...

...#+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, I Pi Pz Pn-i...

...an inferior limit of the positive roots of an equation, that is a number which is not greater than any of the positive roots. For transform the proposed...equation. Thus suppose the proposed equation to be put — for x, and multiply by y" and divide by pn, so that the if transformed equation is . 1 «ta...

...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;"...