If three distinct numbers $a, b, c$ are in G.P. and the equations $a x^2+2 b x+c=0$ and $d x^2+2 e x+f=0$ have $a$ common root, then which one of the following statements is correct?
Select the correct option:
A
d, e, f are in A.P.
B
$\frac{d}{a}, \frac{e}{b}, \frac{f}{c}$ are in G.P.
C
$\frac{d}{a}, \frac{e}{b}, \frac{f}{c}$ are in A.P.
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