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`

Three lines px + qy+r=0, qx + ry+ p = 0 and rx + py + q = 0 are concurrent of

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 (a-x)/(p x)=(a-y)/(q y)=(a-z)/ra n dp ,q ,a n dr are in A.P., then prove that x ,y ,z are in H.P.

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 , then p,q,r are in ………………….. .

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.

If the root of x^3+px^2+qx+r=0 are in H.P. prove that 9 pqr = 27 r^2+2q^3 . Assume p,q,r ne 0

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 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