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

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 the equations x^(2) -px +q=0 and x^(2)+qx-p=0 have a common root, then which one of the following is correct?

Prove that if the equations x^2+px+r=0 and x^2+rx+p=0 have a common root then either p=r or , 1+p+r=0.

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 the equations px^(2)+qx+r=0 and rx^(2)+qx+p=0 have a negative common root then the value of (p-q+r)=

Show that the equations px^2+qx+r=0 and qx^2+px+r=0 will have a common root if p+q+r=0 or, p=q=r.

Prove that, if the equations x^2+px+qr=0 and x^2+qx+pr=0[pneq,rne0] have a common root , then p+q+r=0.