Mildly Insane

Algebra Level 4

\[f(x) = \displaystyle \sum_{i=1}^{50}(x+2i-1)(x+2i)\]

Let \(f(x)\) be defined as the function above. Denote \(S\) as the sum of the roots of \(f(x)\) and \(P\) as the product of its roots. Find \( \lfloor S+P \rfloor \).

This is an original problem.
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