For real numbers $$\alpha$$ and $$\beta$$ , let $$p(x) = x^{2} - (\alpha + \beta) x + \alpha \beta$$ and $$q(x) = x^{2} - (\alpha + \beta + 2) x +(\alpha + 1)(\beta + 1)$$. Which of the following statements is true?

The coefficient of the x term in a quadratic equation represents the sum of roots, while the constant term indicates the products of roots. Directly for the P(x) $$\alpha,\ \beta\ $$ are the roots. In q(x), the x coefficient can be written as $$\alpha\ +1+\beta\ +1$$. By this, we say $$\alpha\ +1,\beta\ \ +1$$ are the roots of q(x).

Now, check with the options where the root of p(x) is one less than q(x). It is option C.