If p , q, r are in G.P and the equation px^2 + 2qx + r = 0 and dx^2 + 2ex + f = 0 have a common root , then show that d/p , e/q , f/r are in A.P.

As, p,q,r are in G.P.

Now, On solving the equation (ii) for x, we get,

Putting the value of (i), we get,

∴Equation (ii) has both roots equal, each equal

.................(iv)

This value of x must satisfy the equation (iii) 

 

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