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Inequality equation help

  1. Sep 6, 2010 #1
    Hi everyone,

    1. The problem statement, all variables and given/known data

    P(X)=Xp-1*(X-1)p*...*(X-n)p

    j is an integer between 1 and n;
    x a real beatween 0 and 1.

    Prove that abs(P(jx))<=(n!)p
    2. Relevant equations



    3. The attempt at a solution

    I tried to find an inequality for each abs(jx-q) but the problem is that I can't control j*x...


    Any clue is welcome!
     
  2. jcsd
  3. Sep 6, 2010 #2

    Mark44

    Staff: Mentor

    Re: inequality

    Please show us what you've tried. In particular, what do you have for P(jx)?
     
  4. Sep 6, 2010 #3
    Re: inequality

    For p(jx), you mean?:
    P(jx)=(jx)p-1*(jx-1)p...(jx-n)p

    I wanted to find an inequality for each abs((jx-q)), but my problem is that since jx is between 0 and n, I don't know the sign of jx-q...

    I also tried:
    * abs(jx-q)<=q, but this inequality is obviously wrong(for q=5, x=1 and j=11)...

    *abs(P(jx))<=abs(P(j)) or abs(P(jx))<=abs(P(n*x)) so I could get rid of x or of j,but here too, these inequalities appears to be wrong...
     
    Last edited: Sep 6, 2010
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