# Too many monics

Algebra Level 5

Monic quadratic polynomials $$P(x)$$ and $$Q(x)$$ have the property that $$P(Q(x))$$ has zeros at $$x = -23, -21, -17,$$ and $$-15$$, and $$Q(P(x))$$ has zeros at $$x = -59, -57, -51,$$ and $$-49$$. What is the sum of the minimum values of $$P(x)$$and $$Q(x)$$ ?

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