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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?
 2 years ago
 2 years 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?
 2 years ago
 2 years 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
 2 years 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
 2 years ago

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

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

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

math>philosophy Group TitleBest ResponseYou've already chosen the best response.0
factor
 2 years 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. :(
 2 years 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..
 2 years 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..
 2 years 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
 2 years ago
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