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 a, b, c are in GP , then the equations ax^2 +2bx+c = 0 and dx^2 +2ex+f =0 have a common root if d/a , e/b , f/c are in

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.

If the equation x^2 + px + q =0 and x^2 + p' x + q' =0 have common roots, show that it must be equal to (pq' - p'q)/(q-q') or (q-q')/(p'-p) .

If p and q are the roots of the equation x^(2)+px+q=0 , then

Three lines px + qy+r=0, qx + ry+ p = 0 and rx + py + q = 0 are concurrent of

If the roots of the equation (q-r)x^(2)+(r-p)x+p-q=0 are equal, then show that p, q and r are in A.P.

If p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P.

If the equation x^2-3p x+2q=0a n dx^2-3a x+2b=0 have a common roots and the other roots of the second equation is the reciprocal of the other roots of the first, then (2-2b)^2 . a. 36p a(q-b)^2 b. 18p a(q-b)^2 c. 36b q(p-a)^2 d. 18b q(p-a)^2