IF one root of the equation `px^2+qx+r=0` is the cube of the other, prove that ,`rp(r+p)^2=(q^2-2rp)^2`.

If one of the root of the equation px^2 + qx + r = 0 is the cube of the other, prove that. rp(r + p)^2 = (q^2 - 2rp)^2 .

In the equation x^2-px+q=0 one root is twice of other then prove that 2p^2=9q

If the roots of the equation px^(2)+qx+r=0 are in the ratio l:m then

If the roots of the equation px^(2)+qx+r=0(pne0) be equal, then q=2sqrt(pr) .

If a,b,c are the roots of the equation x^3+px^2+qx+r=0 such that c^2=-ab show that (2q-p^2)^3. r=(pq-4r)^3 .

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 x^(3) - px^(2) + qx - r = 0 are in A.P., then prove that, 2p^3 −9pq+27r=0

If one of the roots of the equation px^(2)+qx+r=0 is three times the other, then which one of the following relations is correct ?

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 alpha,beta are the roots of the equation px^(2)-qx+r=0, then the cquation whose roots are alpha^(2)+(r)/(p) and beta^(2)+(r)/(p) is