A) d, e, ? are in A.P.
B) \[\frac{d}{a},\frac{e}{b},\frac{f}{c}\]a b c are in G.P.
C) \[\frac{d}{a},\frac{e}{b},\frac{f}{c}\]are in A.P.
D) d, e, ? are in G.P.
Correct Answer: C
Solution :
a, b, c in G.P. \[say\,a,\,ar,\,a{{r}^{2}}\] satisfies \[a{{x}^{2}}+2bx+c=0\]\[\Rightarrow \]\[x=-r\] \[x=-r\]is the common root, satisfies second equation \[d(-{{r}^{2}})+2e(-r)+f=0\] \[\Rightarrow \]\[d.\frac{c}{a}-\frac{2ce}{b}+f=0\]\[\Rightarrow \]\[\frac{d}{a}+\frac{f}{c}=\frac{2e}{b}\]You need to login to perform this action.
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