Researches Respecting the Imaginary Roots of Numerical Equations Being a Contin
Researches Respecting the Imaginary Roots of Numerical Equations Being a Contin
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3 + 33a? 2 — 38a? + 4 =0 as in the same method of Budan, this being the transformed equation at which we arrive by diminishing the roots of the reci- procal of the proposed equation by 2. It is to this transformed reciprocal that the development recommended in precept 3, or in the rule at page 20, is to be applied ; * and the operation is as follows : — * In applying the rule at page 20, it will perhaps be advisable, even when the interval is an extreme one, always to employ, as a preliminary, ...Budan's reciprocal transformation, before proceeding with the actual development; or at least to execute as much of this transformation as may be necessary to enable us to foresee whether or not the resulting signs will all be plus. If the entire transformation be effected, we may then apply our development either to this or to the original — if the same number of variations occur in both — which- ever appears to offer the greater facility. As respects the equation above, we may remark that had Budan's method been applied to it as at page 202 of (he Equations, as far as the transformation (6)', and then our criterion of imaginary roots, the analysis would have been completed at that step.
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To quickly assess the difficulty of the text, read a short excerpt:
3 + 33a? 2 — 38a? + 4 =0 as in the same method of Budan, this being the transformed equation at which we arrive by diminishing the roots of the reci- procal of the proposed equation by 2. It is to this transformed reciprocal that the development recommended in precept 3, or in the rule at page 20, is to be applied ; * and the operation is as follows : — * In applying the rule at page 20, it will perhaps be advisable, even when the interval is an extreme one, always to employ, as a preliminary, ...Budan's reciprocal transformation, before proceeding with the actual development; or at least to execute as much of this transformation as may be necessary to enable us to foresee whether or not the resulting signs will all be plus. If the entire transformation be effected, we may then apply our development either to this or to the original — if the same number of variations occur in both — which- ever appears to offer the greater facility. As respects the equation above, we may remark that had Budan's method been applied to it as at page 202 of (he Equations, as far as the transformation (6)', and then our criterion of imaginary roots, the analysis would have been completed at that step.
What to read after Researches Respecting the Imaginary Roots of Numerical Equations Being a Contin?
You can find similar books in the "Read Also" column, or choose other free books by J R John Radford Young to read onlineMoreLess
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