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.

The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are

If p and q are the roots of the equation x^(2)+px+q=0 , then

If the roots of equation x^3+px^2+qx+r=0 are in A.P then show that 2p^3-9pq+27r = 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:

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 ………………….. .