Let $$\alpha, \beta$$ be the roots of the equation $$x^2 - px + r = 0$$ and $$\frac{\alpha}{2}, 2 \beta$$ be the roots of the equation $$x^2 - qx + r = 0$$. Then the value of r is

A

$$\frac{2}{9}(p - q)(2q - p)$$

B

$$\frac{2}{9}(q - p)(2p - q)$$

C

$$\frac{2}{9}(q - 2p)(2q - p)$$

D

$$\frac{2}{9}(2p - q)(2q - p)$$