KöMaL problem A, 2015

Algebra Difficulty 6.0 National Olympiad Prove it Hungary

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

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