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.

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