Equation with Absolute Value!

Algebra Level 4

\[ \large \dfrac{|x|}{x} + x^2 = 2\]

Let \(r_i\) be the roots of the following equation, for \(i = 1 , 2 \ldots, n \) with n as the number of roots of the equation above.

Evaluate \( \displaystyle \sum_{i=1}^n \text{sgn} (r_i) \cdot r_i^2 \).

Notation: \( \text{sgn}(x) \) denote the signum function, \(\begin{cases} sgn(x) =1, x > 0 \\ sgn(x) = 0 , x = 0 \\ sgn(x) = -1 , x < 0 \end{cases}\).

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