Let $P$ be a homogenous polynomial with real coefficients in several variable(at least three variable) Is the following statement true:

For every $\epsilon$ there is a $\delta$ such that for every x with $|P(x)|< \delta$ we have $d(x,Z)<\epsilon$.

Here $Z=P^{-1}(\{0\})$ is the set of roots of $P$, and $d$ is the standard .distance