# Inequality equation help

Hi everyone,

## Homework Statement

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

## 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
Mentor

Hi everyone,

## Homework Statement

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

## 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)?

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...

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