IR-MO 2004 Problem 12

$\mathbb{N}_{10}$ is generalization of $\mathbb{N}$ that every hypernumber in $\mathbb{N}_{10}$ is something like: $\overline{...a_2a_1a_0}$ with $a_i \in {0,1..9}$ (Notice that $\overline {...000} \in \mathbb{N}_{10}$ ) Also we easily have $+,*$ in $\mathbb{N}_{10}$ . first $k$ number of $a*b$ = first $k$ nubmer of (first $k$ number of a * first $k$ number of b) first $k$ number of $a+b$ = first $k$ nubmer of (first $k$ number of a + first $k$ number of b) Fore example $\overline {...999}+ \overline {...0001}= \overline {...000}$ Prove that every monic polynomial in $\mathbb{N}_{10}[x]$ with degree $d$ has at most $d^2$ roots.