`a,b,c` are positive real numbers forming a G.P. If `ax^2+2bx+c=0`and `x^2+2ex+f=0` have a common root, then prove that `d/a, e/b, f/c` are in A.P.

Explanation

Given,


`a, b, c` in G.P.


Geometric mean relation:


`b^2 = ac`


`b=sqrt(ac)`` \ \ \ (1)`


Quadratic equation is given:


`ax^2+2bx+c = 0`` \ \ \ (2)`


Put eq `(1)` in above equation


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