Mod, Oh my God!

Algebra Level 3

Let,
\(\displaystyle f(x) = x^2-5x+6\)
\(\displaystyle g(x) = f(|x|)\)
\(\displaystyle h(x) = |g(x)|\)

Find the set of values of \(\displaystyle \mu\), such that the equation \(\displaystyle h(x)-\mu=0\) has exactly \(\displaystyle 8\) real and distinct roots.

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