Is there any easy proof or/and reference for the following

**Proposition.** If a polynomial $f\in \mathbb{R}[x_1,\dots,x_n]$ with zero constant term has isolated local minimum in 0, then $|f|> C (x_1^2+\dots +x_n^2)^N$ in some neighborhood of 0, where

$\bullet$ $N$ depends only on degree of $f$ and $n$,

$\bullet$ $C$ depends on uniform bound on $n$, degree of $f$, and bounds for coefficients of $f$.

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