# 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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