Question 25
Assume that $n$ is a positive integer, and a polynomial
$$P(x)=a_{2n}x^{2n}+a_{2n-1}x^{2n-1}+\dots+a_1x+a_0$$
satisfies $100\le a_i\le101$ for all $0\le i\le2n$. Find the least possible $n$ such that this polynomial may have a real root.
$$P(x)=a_{2n}x^{2n}+a_{2n-1}x^{2n-1}+\dots+a_1x+a_0$$
satisfies $100\le a_i\le101$ for all $0\le i\le2n$. Find the least possible $n$ such that this polynomial may have a real root.