# Firecracker!

Algebra Level 4

Let $$p(x) = x^2-5x +a$$ and $$q(x) = x^2-3x+ b$$ where $$a$$ and $$b$$ are positive integers. Suppose $$\gcd(p(x), q(x)) = x- 1$$ and denote $$k(x) = \text{lcm}(p(x),q(x))$$. Find the sum of all distinct roots of $$(x-1) + k(x)$$.

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