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If three distinct numbers \( a, b \) and \( c \) are in GP and the equations \( a x^{2}+2 b x+c=0 \) and \( d x^{2}+2 e x+f=0 \) have a
\( \mathrm{P} \) common root, then which one of the following statements is correct?
(2019 Main, 8 April II)
W
(a) \( d, e \) and \( f \) are in \( \mathrm{GP} \)
(b) \( \frac{d}{a}, \frac{e}{b} \) and \( \frac{f}{c} \) are in \( \mathrm{AP} \)
(c) \( d, e \) and \( f \) are in \( \mathrm{AP} \)
(d) \( \frac{d}{a}, \frac{e}{b} \) and \( \frac{f}{c} \) are in GP
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