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If a, b, c are in geometric progresion a...

If `a`, `b`, `c` are in geometric progresion and the roots of the equations `ax^(2)+2bx+c=0` are `alpha` and `beta` and those of `cx^(2)+2bx+a=0` are `gamma` and `delta` then

A

`alpha ne beta ne gamma ne delta`

B

`alpha ne beta` and `gamma ne delta`

C

`a alpha = a beta = c gamma = c delta`

D

`alpha=beta` , `gamma ne delta`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` Because `b^(2)=ac`, the roots of both the equations are equal.
`:.alpha=beta` and `gamma=delta`.
But `gamma=(1)/(alpha)` and `delta=(1)/(beta)` as the given equations are reciprocal to each other.
`:.gammadelta=(a)/(c )`, then `c gamma=a beta`
`:. a alpha=a beta=c gamma=c delta`
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