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Numbers Universalized Volume 2; An Advanced Algebra

Numbers Universalized Volume 2; An Advanced Algebra


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1890 Excerpt: ...method of solution to equations before the commensurable roots have been removed by division, on account of the great labor involved in deriving and evaluating the different functions when the equation is of a high degree, yet such a course may be pursued. If there are equal roots, the fact will appear in deriving the functions, and if there are integral or fractional roots they will be discovered in evaluating the functions to determine their signs. Example.--Determine the number and situation of the real roots in f3 (x) = x3--12 x2 + 57 x-94 = 0. Solution: /, (x) = x-12 x + 57 x-94 f, (x) = 3a;j-24a; + 57 f, (x)=-x + 3 /.(&) = Substituting in these functions as follows, we shall have: For a; = + oo, + +----one variation. For x = 0, --+ +--two variations. For x =--oo, --+ +--two variations. There is, therefore, one real root between 0 and + oo. There is no negative root. Therefore, there are two imaginary roots. To find the situation of the real root, we proceed as follows: For x = 1, we have--+ +--two variations. For x--2, we have--+ +--two variations. For x = 3, we have--+ --two variations. For x = 4, we have + +----one variation. Therefore, there is one real root between 3 and 4, or the first figure of the real root is 3. To find the next figure, we proceed as follows: For x--3'1, we have--+----two variations. For x = 3-2, we have--+----two variations. For x = 3-3, we have--+----two variations. For x = 3-4, we have + +----one variation. Therefore, the root lies between 3;3 and 3-4, or the first two figures of the root are 3-3. By a continuation of this process the root might be extended to any number of figures. A more expeditious method, however, is known, and will be explained hereafter, for extending a root after a sufficient number of figures


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Product Details
  • ISBN-13: 9781130518184
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 28
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1130518183
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 68 gr


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