Let the arithmetic mean of $$\dfrac{1}{a}$$ and $$\dfrac{1}{b}$$ be $$\dfrac{5}{16}$$, $$\text{a > 2}$$. If $$\alpha$$ is such that $$ a,\alpha,b $$ are in A.P., then the equation $$\alpha x^{2}-ax+2(\alpha-2b)=0$$ has:

A

one root in (1, 4) and another in (- 2, 0)

B

complex roots of magnitude less than 2

C

both roots in the interval (- 2, 0)

D

one root in (0, 2) and another in (- 4, - 2)