[ Example 24 If p,q,r are in G.P.and the equations,px^(2)+2qx+r=0 and dx^(2)+2ex+f=0 have a common root,then show that (d)/(p),(e)/(a),(f)/(r) are in A.P.]

If p,q,r are in G.P. and the equations, 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.

If p,q,r are in G.P. and the equations, 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.

If p,q,r are in G.P. and the equations, 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.

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

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

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

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 AP.

If a, b, c are in G.P. and the equation ax^(2) + 2bx + c = 0 and dx^(2) + 2ex + f = 0 have a common root, then show that (d)/(a), (e)/(b), (f)/(c ) are in A.P.

If the equations px^2+2qx+r=0 and px^2+2rx+q=0 have a common root then p+q+4r=

If the equations px^2+2qx+r=0 and px^2+2rx+q=0 have a common root then p+q+4r=