Let $$a_{1} a_{2}, a_{2}$$ be three distinct real numbers in geometric progression. If the equations $$a_{1}x^{2} + 2a_{2} x + a_{3} = 0$$ and $$b_{1}x^{2} + 2b_{2}x + b_{3} = 0$$ has a common root,then which of the following is necessarily true?

A

$$b_{1}, b_{2}, b_{3}$$ are in arithmetic progression

B

$$\frac{b_{1}}{a_{1}}, \frac{b_{2}}{a_{2}}, \frac{b_{3}}{a_{3}}$$ are in arithmetic progression

C

$$b_{1}, b_{2}, b_{3}$$ are in geometric progression

D

$$\frac{b_{1}}{a_{1}}, \frac{b_{2}}{a_{2}}, \frac{b_{3}}{a_{3}}$$ are in geometric progression