If `p(q-r)x^2+q(r-p)x+r(p-q)=0` has equal roots, then prove that `2/q=1/p+1/rdot`

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.

Prove that p x^(q-r)+q x^(r-p)+r x^(p-q)> p+q+r ,w h e r ep ,q ,r are distinct and x!=1.

If lines p x+q y+r=0,q x+r y+p=0a n dr x+p y+q=0 are concurrent, then prove that p+q+r=0(w h e r ep ,q ,r are distinct )dot

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.

If the roots of the equation q^(2)x^(2)+p^(2)x+r^(2)=0 are the squares of the roots of the equation qx^(2)+px+r=0 , are the squares of the roots of the equation qx^(2)+px+r=0 , then q, p, r are in: