Primitive Modular Quadratics. Part I

Algebra Level 3

\[\text{Let} : \quad \begin{cases} \quad f(x)=x^2-6x-16 \\ \ \ \ \ g(x)=f(|x|) \\ \ \ \ \ h(x)=|g(x)| \end{cases} \]

Find the sum of all real roots of the equation \(g(x)=0\).

Author's Note : What you observe in the picture attached to this problem?

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