Largest Root of a Product of Polynomials

The largest rational root of a polynomial $ f(x) $ is 2, while the largest rational root of a polynomial $ g(x) $ is -5. What is the largest rational root of the polynomial $ f(x) \cdot g(x)^2 $? The answer is in the form $\frac{\alpha}{\beta}$ where $\alpha$ and $\beta$ are coprime positive integers. Input the value of $\alpha + \beta$.