1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proving a formula

  1. Mar 2, 2008 #1
    1. The problem statement, all variables and given/known data
    Prove that if p(x)=anx^n +an-1x^n-1+..........a0, where a0,.........., "an" ε reals, is a polynomial, then p can have at most n roots.


    2. Relevant equations



    3. The attempt at a solution

    C ε R is a root of a polynomial p if p(c)=0. If c is a root of p, then x-c is a factor of p.

    I'm not sure where to go from here. I think it would probably be the easiest to prove this by proving the contrapositive as being false. Could someone please give me a hint or show me where to go from here?

    Thank you very much
     
  2. jcsd
  3. Mar 2, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Sure. Suppose the polynomial has n+1 different roots. c1,c2,...cn+1. Since c1 is a root the polynomial p(x) can be factored (x-c1)*p1(x) where p1 has degree n-1. The other c's must be roots of p1(x) since they aren't roots of (x-c1). Continue in this way until you reach degree 1. Now you have a linear polynomial with two different roots. Possible?
     
  4. Mar 2, 2008 #3
    Thank you very much

    Would it be somthing like this?

    (p1x)^(n-1)(x-c2)(x-c3)^(n) :confused:

    Thank you
     
    Last edited: Mar 2, 2008
  5. Mar 2, 2008 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    No, that's not clear at all. Start by proving if n=1 then the polynomial can't have 2 roots. Ok?
     
  6. Mar 5, 2008 #5
    Thank you very much

    Regards
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Proving a formula
Loading...