1. The problem states that $\alpha$ and $\beta$ are the roots of a quadratic equation. We need to find relationships involving these roots. 2. For a quadratic equation of the form $ax^2 + bx + c = 0$, the sum and product of roots are given by: $$\alpha + \beta = -\frac{b}{a}$$ $$\alpha \beta = \frac{c}{a}$$ These are important because they allow us to relate the coefficients of the equation to its roots. 3. If you provide the specific quadratic equation, we can substitute the values of $a$, $b$, and $c$ to find $\alpha + \beta$ and $\alpha \beta$. 4. Without the specific equation, the general formulas above are the key results involving the roots $\alpha$ and $\beta$.