For every positive integer $n$, we consider the polynomial of real coefficients, of $2n+1$ terms, $$P(x)=a_{2n}x^{2n}+a_{2n-1}x^{2n-1}+...+a_1x+a_0$$where all coefficients are real numbers satisfying $100 \le a_i \le 101$ for $0 \le i \le 2n$. Find the smallest possible value of $n$ such that the polynomial can have at least one real root.