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Question

If a,b,c are in G.P, then the equations, ax2+2bx+c=0 and dx2+2ex+f=0 have a common root if da,eb,fc are in

A
A.P
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B
G.P
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C
H.P
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D
None of these
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Solution

The correct option is A A.P
Let a,b,c be in G.P.

b2=ac
Also, ax2+2bx+c=0
ax2+2acx+c=0
((a)x+c)2=0
(a)x+c=0
x=ca
ca is a root of dx2+2ex+f=0
d(ca)2eca+f=0
da2e1ac+fc=0
2eb=da+fc
da,fc,eb are in A.P.

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