`a ,b ,c` are positive real numbers forming a G.P. ILf `a x 62+2b x+c=0a n ddx^2+2e x+f=0` have a common root, then prove that `d//a ,e//b ,f//c` are in A.P.

a ,b ,c are positive real numbers forming a G.P. ILf a x^2+2b x+c=0a n ddx^2+2e x+f=0 have a common root, then prove that d//a ,e//b ,f//c are in A.P.

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

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

a,b,c are positive real numbers forming a G.P. ILf 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.

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

a,b,c are positive real numbers forming a G.P. ILf 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.

a,b,c are positive real numbers forming a. G.P. If ax ^(2) + 2 bx + c=0 and dx ^(2) + 2 ex + f =0 have a common root, pairs (a,b) of real numbers such that d/a,e/b,f/c are in arithmetic progression.

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.