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

Options

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`

Answer

C

Explanation

`(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`