If the roots of `x^3+px^2+qx+r=0` are in GP find the relation between `p,q and r`

If the ratio of the roots of the equation x^2-px+q=0 be 1:2 , find the relation between p and q.

Given that roots of x^3+3px^2+3qx+r=0 are in G.P. show that p^3 r=q^3

If alpha , beta , gamma are the roots of x^3 +px^2 +qx +r=0 then find sum alpha^3

If alpha , beta , gamma are the roots of x^3 +px^2 +qx +r=0 then find sum alpha^3

If alpha , beta , gamma are the roots of x^3 +px^2 +qx +r=0 then find sum alpha^2

If alpha , beta , gamma are the roots of x^3 +px^2 +qx +r=0 then find sum alpha^2

show that the condition that the roots of x^3 + 3 px^2 + 3 qx +r=0 may be in h.P is 2q^3=r (3 pq -r)

show that the condition that the roots of x^3 + 3 px^2 + 3 qx +r=0 may be in h.P is 2q^3=r (3 pq -r)

If the roots of the quadratic equation px^(2)+qx+r=0 are reciprocal to each other ,then the relation between p and r is