If $a, b, c$ are in $GP$ and equations $ax^2+2bx+c=0$ and $dx^2+2ex+f=0$ have a common root, then $\large\frac{d}{a}$, $\large\frac{e}{b}$, $\large\frac{f}{c}$ are in

Question

$(a)\;AP\qquad(b)\;GP\qquad(c)\;HP\qquad(d)\;None\;of\;these$