Beecrofts General Method of Finding All the Roots Both Real And Imaginary of a
Beecrofts General Method of Finding All the Roots Both Real And Imaginary of a
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In our eReader you can find the full English version of the book. Read Beecrofts General Method of Finding All the Roots Both Real And Imaginary of a Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Beecrofts General Method of Finding All the Roots Both Real And Imaginary of a
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Take y negative then (33) becomes, ♦ /+3/+5/-/-3/-2/ + l = (36) This equation contains two roots less than their reciprocals, and decreasing these roots, according to the first method of transformation, 2/i + l by substituting y= — - —, we get the equation yl + Uyl + 652/j + 152^/^ + 123?/^ - 36y^+ 3 = 0, and denoting this equation by/(?/j) = 0, we get 21 ^ =l + 122/j + lOSy] + 693i2/i + ^^^^32/^ + 7698|2/^' -87185|2/i -&c. Multiplying these coefficients by 3, we may take a =309, « =2080, « =10...402, ^ =28096, and substituting these values in the general equation (15) forwi = 5, we get 601619242/j -14499496y^ + 1112182 = 0.
Similarly by proceeding another step we get 9762412988^^ - 23528473762/^ + 180485772 = 0, . Or, ijI -•2410108?/^+-0184878 = 0..... (37) The preceding equation gives, when divided by its first coefficient, yl -•24100782/j + -0184864 = 0, which will give the same roots as (37) to five places of figures, and I believe (37) to be exact to the last figure; it can-however be easily tested by extending the above division another term.
What to read after Beecrofts General Method of Finding All the Roots Both Real And Imaginary of a?
You can find similar books in the "Read Also" column, or choose other free books by Philip Beecroft to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Take y negative then (33) becomes, ♦ /+3/+5/-/-3/-2/ + l = (36) This equation contains two roots less than their reciprocals, and decreasing these roots, according to the first method of transformation, 2/i + l by substituting y= — - —, we get the equation yl + Uyl + 652/j + 152^/^ + 123?/^ - 36y^+ 3 = 0, and denoting this equation by/(?/j) = 0, we get 21 ^ =l + 122/j + lOSy] + 693i2/i + ^^^^32/^ + 7698|2/^' -87185|2/i -&c. Multiplying these coefficients by 3, we may take a =309, « =2080, « =10...402, ^ =28096, and substituting these values in the general equation (15) forwi = 5, we get 601619242/j -14499496y^ + 1112182 = 0.
Similarly by proceeding another step we get 9762412988^^ - 23528473762/^ + 180485772 = 0, . Or, ijI -•2410108?/^+-0184878 = 0..... (37) The preceding equation gives, when divided by its first coefficient, yl -•24100782/j + -0184864 = 0, which will give the same roots as (37) to five places of figures, and I believe (37) to be exact to the last figure; it can-however be easily tested by extending the above division another term.
What to read after Beecrofts General Method of Finding All the Roots Both Real And Imaginary of a?
You can find similar books in the "Read Also" column, or choose other free books by Philip Beecroft to read onlineMoreLess
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