IF ` x^2 +px + q=0` and ` x^2 + qx +p=0` have a common root , then their other roots are the roots of

IF every pair from the equation x^2 +px +qr =0 , x^2 +qx + rp =0 and x^2 + rx +pq =0 has a common root , them the product of three common roots is

If x^(2)+px+q=0 and x^(2)+qx+p=0 have a common root, prove that either p=q or 1+p+q=0 .

If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that p+q=0 . Also, show that their other roots are the roots of the equation x^2+x+p q=0.

If the equation x^(2)+qx+rp=0 and x^(2)+rx+pq=0 have a common root,,then the other root will satisfy the equation

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 . Also, show that their other roots are the roots of the equation x^2+x+p q=0.