Lessons On Higher Algebra: With An Appendix On the Nature of Mathematical Reasoning
Lessons On Higher Algebra: With An Appendix On the Nature of Mathematical Reasoning
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In our eReader you can find the full English version of the book. Read Lessons On Higher Algebra: With An Appendix On the Nature of Mathematical Reasoning 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 Lessons On Higher Algebra: With An Appendix On the Nature of Mathematical Reasoning
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To quickly assess the difficulty of the text, read a short excerpt:
+ 4 when a? = 2.
1 0-2 0+3+4 (2 2 4 4 8 22 2 2 4 11 26 .•./(2) = 26.
Ex. 2. Determine whether —3 is a root of a^4.7aj3 + 5aj*- 31a; -30 = 0.
1 4-7 +5 -31 -30 (-3 -3 -12 21 +30 4 -7 ^^10 Since /(- 3) = 0, - 3 is a root of f{x) = 0.
26. The process of the preceding article also enables us to divide /(a?) by a; — a when a is a root of /(a?) = 0.
Let /(a?) be evaluated for a as before ; the required quo- tient /(«) -J- (a? — a) will be, supposing f{x) is of the fourth degree, a* + (a +i>i)a* + (a^ ...+ Pi" +i>2)» + («* +i>ia* +i>2a +i>8)- The function is one degree lower than /(«); and the coefficients of x after the first are the successive sums obtained in the process of evaluating, the last sum van- ishing, since a is now supposed to be a root of /(a?) = 0.
That this is the quotient when f{x) is divided by a; — a appears at once by multiplying this new function by x — a\ thus: GRAPHS. 81 aj» + (a + jpi)aj* 4- (a* + jPia + 1>2)« + («* 4- !>!«* 4- l>8a 4- 1>8) X* + (a +Pi)a^ + (a' + Pia4-i>2)»* + {c^+PiCt^+P^P^ -^Ps)^ —aa^—{a^'{-Pia)a^--{(^+Pia^-{-p3a)-(a*-{'Pi(^-{'P^^-{'Psa) ^ -VPx^-Vp^ +i>8» - (a* 4-Pia' +i>8a* 4-P3a)- Since a* +i>ia' +i>8a* +i>8« +i>4 = 0, or a* 4-i>ia^ -\-p^ +i>8a = -i>4> we have finally for the product «* ^-Px^ +P^ 4-i>8» +i>4, the original function.
What to read after Lessons On Higher Algebra: With An Appendix On the Nature of Mathematical Reasoning?
You can find similar books in the "Read Also" column, or choose other free books by Ellen Hayes to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
+ 4 when a? = 2.
1 0-2 0+3+4 (2 2 4 4 8 22 2 2 4 11 26 .•./(2) = 26.
Ex. 2. Determine whether —3 is a root of a^4.7aj3 + 5aj*- 31a; -30 = 0.
1 4-7 +5 -31 -30 (-3 -3 -12 21 +30 4 -7 ^^10 Since /(- 3) = 0, - 3 is a root of f{x) = 0.
26. The process of the preceding article also enables us to divide /(a?) by a; — a when a is a root of /(a?) = 0.
Let /(a?) be evaluated for a as before ; the required quo- tient /(«) -J- (a? — a) will be, supposing f{x) is of the fourth degree, a* + (a +i>i)a* + (a^ ...+ Pi" +i>2)» + («* +i>ia* +i>2a +i>8)- The function is one degree lower than /(«); and the coefficients of x after the first are the successive sums obtained in the process of evaluating, the last sum van- ishing, since a is now supposed to be a root of /(a?) = 0.
That this is the quotient when f{x) is divided by a; — a appears at once by multiplying this new function by x — a\ thus: GRAPHS. 81 aj» + (a + jpi)aj* 4- (a* + jPia + 1>2)« + («* 4- !>!«* 4- l>8a 4- 1>8) X* + (a +Pi)a^ + (a' + Pia4-i>2)»* + {c^+PiCt^+P^P^ -^Ps)^ —aa^—{a^'{-Pia)a^--{(^+Pia^-{-p3a)-(a*-{'Pi(^-{'P^^-{'Psa) ^ -VPx^-Vp^ +i>8» - (a* 4-Pia' +i>8a* 4-P3a)- Since a* +i>ia' +i>8a* +i>8« +i>4 = 0, or a* 4-i>ia^ -\-p^ +i>8a = -i>4> we have finally for the product «* ^-Px^ +P^ 4-i>8» +i>4, the original function.
What to read after Lessons On Higher Algebra: With An Appendix On the Nature of Mathematical Reasoning?
You can find similar books in the "Read Also" column, or choose other free books by Ellen Hayes to read onlineMoreLess
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