# Bound A Sum Of Squares - Not As Easy As You Think

Algebra Level 5

Consider polynomials of the form $$x^{2014} + a_{2013} x^{2013} + \ldots + a_1x + 1$$, with real coefficients and having at least one real zero. Determine the smallest possible value of $$\sum_{i=1}^{2013} a_i^2$$.