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 alpha,beta,gamma are the roots of the equation x^(3)+px^(2)+qx+r=0 such that alpha+beta=0 then

If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then

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

Discuss the signs of the roots of the equation px^(2)+qx+r=0

If (a)/(k),a, ak are the roots of x^(3)-px^(2)+qx-r=0 then a=

If p, q, r are the roots of the equation x^3 -3x^2 + 3x = 0 , then the value of |[qr-p^2, r^2 , q^2],[r^2,pr-q^2,p^2],[q^2,p^2,pq-r^2]|=

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

If alpha,beta are the roots of the equation px^(2)-qx+r=0, then the equation whose roots are alpha^(2)+(r)/(p) and beta^(2)+(r)/(p) is (i) p^(3)x^(2)+pq^(2)x+r=0 (ii) px^(2)-qx+r=0 (iii) p^(3)x^(2)-pq^(2)x+q^(2)r=0 (iv) px^(2)+qx-r=0