Question 7
Find the smallest positive integer $n$ for which a polynomial
$$P(X)=a_{2n}X^{2n}+a_{2n-1}X^{2n-1}+\ldots+a_1X+a_0$$
with real coefficients has both properties:
- $2014\le a_i\le2015$ for $i=0,1,\ldots,2n$;
- there is a real number $\xi$ such that $P(\xi)=0$.
$$P(X)=a_{2n}X^{2n}+a_{2n-1}X^{2n-1}+\ldots+a_1X+a_0$$
with real coefficients has both properties:
- $2014\le a_i\le2015$ for $i=0,1,\ldots,2n$;
- there is a real number $\xi$ such that $P(\xi)=0$.