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Question

If a, b and c are in G.P., then the quadratic 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.
ax2+2bx+c=0
D=4b24ac=0 (as a, b, c are in G.P.)
equation has equal roots which are equal to ba each.

Thus, it should also be the root of dx2+2ex+f=0
d(ba)2+2e(ba)+f=0
db2a22bea+f=0
daca22bea+f=0 (as b2=ac)
da+fc=2ebac=2eb

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