# 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 \( \sum_{i=1}^{2013} a_i^2 \).

**Round your answer to 3 decimal places.**