Mod, Oh my God!

Algebra Level 4

Let,
f(x)=x25x+6\displaystyle f(x) = x^2-5x+6
g(x)=f(x)\displaystyle g(x) = f(|x|)
h(x)=g(x)\displaystyle h(x) = |g(x)|

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

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