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Polynomials help

  1. Feb 21, 2012 #1
    Polynomials help~~

    Heh, so I posted this thread in the wrong category so I'm reposting it! =)
    Hello. So here was this problem I came across:

    If x^4-x^3+x^2-x^1+x^0=0, what is the numerical value of x^40-x^30+x^20-x^10+x^0?
    I did try doing many stuffs (symmetry) & factoring, but I think none of these steps helped.
    Enlighten the youngster, gracias.
     
  2. jcsd
  3. Feb 21, 2012 #2
    Re: Polynomials help~~

    If 2X=0, what is 20X?
     
  4. Feb 21, 2012 #3
    Re: Polynomials help~~

    @adaptation -_- very funny, if it was a simple problem like that I wouldn't have posted it.
    Btw, the answer's 1.
    Hmm... but How...?
     
  5. Feb 22, 2012 #4
    Re: Polynomials help~~

    I found no shortcut in doing this :uhh: ,
    maybe then the only way to do this is find the roots and put them in the second equation :grumpy: ,
    Yea lengthy it is
     

    Attached Files:

  6. Feb 22, 2012 #5
    Re: Polynomials help~~

    There could be a work around , using roots of unity , you need to think about it .
    ( sum of roots of unity and their properties )
     
  7. Feb 22, 2012 #6

    Deveno

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    Re: Polynomials help~~

    our original polynomial is p(x) = x4-x3+x2-x+1.

    note that p(-1) = 1 + 1 + 1 + 1 + 1 = 5, so -1 is not a root of p(x).

    now consider q(x) = (x+1)p(x) = x5 + 1.

    Mod note: rest of solution removed
     
    Last edited by a moderator: Feb 22, 2012
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