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.

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 the equation x^2+px+qr=0 and x^2+qx+pr=0(p!=q,r!=0) has same root then prove that p+q+r=0

Prove that , if the equations x^2+bx+ca=0 and x^2+cx+ab=0 have only non-zero common root then their other roots satisfy the equation t^2+at+bc=0 .

If the equation x^2+ax+bc=0" and " x^2+bx+ca=0 have a common root, then a+b+c =

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 x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that 1+p+q=0 .

If the equations 2x^(2)-7x+1=0 and ax^(2)+bx+2=0 have a common root, then

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.

The equations x^2+x+a=0 and x^2+ax+1=0 have a common real root

If the roots of the quadratics x^2+2px+q=0 and x^2+2qx+p=0(pneq) differ by a constant, show that p+q+1=0.