Let $f(x)∈mathbb R(x)$ be polynomial over real number.
I think the following claim holds.
$∀x∈mathbb Q$, $f(x)≧0$ implies $∀x∈mathbb R$, $f(x)≧0$
I think this holds because of density of $mathbb Q$ in $mathbb R$.
- Does this claim correct?
- Can we extend this statement to some general results?
Thank you in advance.