If a, b, c are in G.P. and the equations ax2+2bx+c=0=0 and dx2+2ex+f=0 have a common root. Then?
A
d, e, f are in G.P.
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B
d, e, f are in A.P.
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C
ad,be,cf are in A.P.
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D
ad,be,cf are in H.P.
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Solution
The correct option is Dad,be,cf are in H.P. b2=ac roots of ax2+2bx+c=0 are equal i.e., −ba d(−ba)2+2e(−ba)+f=0 db2−2bea+fa2=0 dc−2eb+fa=0 divide by ac dcac−2ebb2+faac=0 ⇒da−2ebb2+faac=0 ⇒da−2eb+fc=0 da,eb,fc are in A.P.