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)