Continuity of a function in a closed and bounded interval and in R

Question

If $h(x)=0 \forall ,x\in [0,1]$ and h be a polynomial then is $h(x)=0 ,\forall x\in \Bbb R$ ? I can't conclude this.

Answer 1

Hint: A non-zero polynomial of degree $n$ has at most $n$ roots.