Primitive Modular Quadratics. Part II

Algebra Level 4

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

Find the max. value of \(A\) such that the equation \(g(x)-A=0\) has exactly three real and distinct roots.

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