Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Is there a quick analytic way to solve this polynomial?

  1. May 23, 2013 #1
    ny = x^(n-1) + x^(n-2) + ... + x + 1

    for a certain y and n (>10000) with y!=1 and ny > 1.

    Is there an analytic way to solve this? Thank you.
  2. jcsd
  3. May 23, 2013 #2
    yes, you can interpret it as a sum. that way you can work with it easily.
    from that point on you can prove any type of given question whatsoever

    Attached Files:

  4. May 23, 2013 #3
    thank you for your reply, my question was though how to find x for let's say y = 4 and n = 10000 in the shortest possible amount of time. i know that's not feasible for polynomials of this size in general, but i don't know if there are any special kinds and solution strategies, since this one looks quite simple.
    i should have added that i am only interested in real solutions which only exist for n*y >= 1.
  5. May 23, 2013 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    I think poster #2 is confused. The OP was looking to solve the polynomial, not take derivatives or integrals.

    AFAIK, there is no simple analytic way to solve polynomials with degree 5 and greater.
  6. May 23, 2013 #5


    User Avatar
    Science Advisor

    The sum on the right = (1-xn)/(1-x).

    Can you go from there?
  7. May 23, 2013 #6
    incredible. thanks a lot!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook