[" (ii) Show that the equations "px^(2)+qx+r=0" and "],[qx^(2)+rx+p=0" will have a common root if "],[p+q+r=0" or,"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.

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=

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)=

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.

if the equation x^(2)+qx+rp=0 and x^(2)+rx+pq=0,(q!=r) have only one root in common, then prove that p+q+r=0 .

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.