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math>philosophy
Group Title
factorize x^5  x + 1 = 0
i'm not sure how to factor beyond the 3rd/4th degree. how do i do this one?
 one year ago
 one year ago
math>philosophy Group Title
factorize x^5  x + 1 = 0 i'm not sure how to factor beyond the 3rd/4th degree. how do i do this one?
 one year ago
 one year ago

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satellite73 Group TitleBest ResponseYou've already chosen the best response.1
fairly sure this will not factor over the rationals, since a quick graph shows it has only one real zero
 one year ago

math>philosophy Group TitleBest ResponseYou've already chosen the best response.0
but how does a "quick graph [that] shows it has one zero" show anything? y=x^5 also has one zero as well. not sure what the point is
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\(y=x^5\) is factored
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
if you can find the zeros then you can factor. i am assuming you mean factor over the rational numbers, although maybe i am mistaken about that
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
i dont spose theres a simple easy way to "complete a quintic"?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
not according to galois
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
you can try newtons method of trial and error to get closer and closer to a real root
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
hmmm  do you really want to factorise this or are you looking for the solutions? if its the solutions you want then use the method suggested by @amistre64
 one year ago

math>philosophy Group TitleBest ResponseYou've already chosen the best response.0
factor
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
the only factorisation I can think of here is as follows:\[\begin{align} x^5x+1&=0\\x(x^41)+1&=0\\ x(x^21)(x^2+1)+1&=0\\ x(x1)(x+1)(x^2+1)+1&=0\\ \end{align}\]but I don't think that helps towards getting to the solution. :(
 one year ago

cinar Group TitleBest ResponseYou've already chosen the best response.0
since f(1)>0 and f(2)<0 one root is between 1 and 2 by the Bolzano theorem..
 one year ago

cinar Group TitleBest ResponseYou've already chosen the best response.0
since it is odd degree poly. we can say that it has at least one real root.. but I do not know how to say it has only one real root without looking its graph and I also wanna learn it..
 one year ago

cinar Group TitleBest ResponseYou've already chosen the best response.0
wow man look at the roots!! http://www.wolframalpha.com/input/?i=factor+x^5x%2B1%3D0 http://www.wolframalpha.com/input/?i=factor+x^5x%2B1
 one year ago
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