Ray's Algebra, Part Second Volume 2; An Analytical Treatise, Designed for High Schools and Colleges
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Ray's Algebra, Part Second Volume 2; An Analytical Treatise, Designed for High Schools and Colleges

Ray's Algebra, Part Second Volume 2; An Analytical Treatise, Designed for High Schools and Colleges


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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. 1857 Excerpt: ...becomes a a x--2px=q. (2) If _ is positive, and C-negative, the equation becomes a a x+2px=--q. (3) b i Lastly, if-and _ are both negative, the equation becomes a a (4) Hence, every complete equation of the second degree, may be reduced to the form x2--2px=q, in which 2p and q may be either positive or negative, integral or fractional quantities. We will now proceed to explain the principle by which the first member of this equation may always be made a perfect square. Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second; if we consider x--2px as the first two terms of the square of a binomial, we find x2 is the square. of the first term; hence, the first term must be x; we next observe that 2px is the double of the product of the first term by the second; therefore, if we divide 2px by x, the quotient 2p is double the second term. Hence p, which is half the coefficient of x, is the second term of the binomial; therefore, its square, '2, added to x+2px, will render it a perfect square. But, to preserve the equality, we must add the same quantity to both sides. This gives, It is obvious that in each of the remaining three forms, the square may be completed on the same principle; that is, by taking half the coefficient of the first power of x, squaring it, and adding it to each member. Solving equations (2), (3), and (4), and collecting together the four different forms, and the values of x in each, we have the following table. (1) a?--2px=q. (2) x--2px=q. (3) x2--2px=--q. (4) x3 Although the method of finding the values of x is the same in each of these forms, it is convenient to distinguish between them. See Art. 235. From the preceding we derive the fol...


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Product Details
  • ISBN-13: 9781156457252
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 84
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1156457254
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 168 gr

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Ray's Algebra, Part Second Volume 2; An Analytical Treatise, Designed for High Schools and Colleges
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