Mathematical and Physical Journal
for High Schools
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# Problem A. 654. (November 2015)

A. 654. Let $\displaystyle p(x)$ be a polynomial of degree at most $\displaystyle n$ such that $\displaystyle \big|p(x)\big|\le\frac{1}{\sqrt{x}}$ for $\displaystyle 0<x\le 1$. Prove that $\displaystyle \big|p(0)\big|\le 2n+1$.

(5 pont)

Deadline expired on December 10, 2015.

### Statistics:

 5 students sent a solution. 5 points: Bukva Balázs, Williams Kada. 3 points: 1 student. 2 points: 1 student. 0 point: 1 student.

Problems in Mathematics of KöMaL, November 2015