If `p,q,r>0` and `p!= q!= r` such that, `f(x) = px^2 + 2qx + r`, `g(x) = qx^2 + 2rx + p`, `f(x) = 0` and `g(x) = 0` has a common root.

If every pair from among the equations x^ 2 + p x + q r = 0, x^2+px+qr=0, x^2 + q x + r p = 0, x^2+qx+rp=0 and x^2 + r x + p q = 0, x^2+rx+pq=0 has a common root then the product of three common root is (A) pqr (B) 2pqr (C) (p^2q^2r^2) (D)none of these

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.

Prove that equations (q-r)x^(2)+(r-p)x+p-q=0 and (r-p)x^(2)+(p-q)x+q-r=0 have a common root.