Inspired by Challenge Master note (Problem is edited)

Algebra Level 3

Evaluate \(\Omega\):

\[ \large \Omega = \displaystyle\sum_{-50}^{49} \text{sgn}(x^2 + 5x + 6) \]

Notations:

  • \(\text{sgn}(x) \) denotes the signum function of \(x\)

  • \( \text{sgn}(x) = \begin{cases} 1 \quad,\quad x>0 \\ 0 \quad,\quad x=0 \\ -1 \quad,\quad x<0 \end{cases} \)

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