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

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

math>philosophy
 3 years ago
Best ResponseYou've already chosen the best response.0but 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

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

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1if 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

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

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1not according to galois

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.0you can try newtons method of trial and error to get closer and closer to a real root

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1hmmm  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

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1the 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. :(

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

cinar
 3 years ago
Best ResponseYou've already chosen the best response.0since 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..

cinar
 3 years ago
Best ResponseYou've already chosen the best response.0wow 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
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