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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