Extracting Polynomial Parameters

Algebra Level 5

Let \( f(x) = 2 x^3 + 5 x^2 - 7 x + 1 \) and \(g(x) = f(x^2 + 5x + 1) \).

If \( \{ s_i \} \) are the roots of \( g(x) \), find the value of the below expression.

\[ \sum_i {s_i}^2 \]

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