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.


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