Proving Inequality for P(X) with Real Variables | Step-by-Step Guide

[penguin007]

Hi everyone,

Homework Statement

P(X)=X^p-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

Homework Equations

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!

 

[Mark44]

Hi everyone,

Homework Statement

P(X)=X^p-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

Homework Equations

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!

Please show us what you've tried. In particular, what do you have for P(jx)?

 

[penguin007]

Please show us what you've tried. In particular, what do you have for P(jx)?

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...