If one root is square of the other  root of the equation x2+px+q=0, then the relation between p and q is

The given equation is x2+px+q=0 Suppose that the roots are α,α2Hence,α+α2=−p,α3=q⇒α=q13Since q13 is one root of the equation            q23+pq13+q=0q13+q23=−pCubing on both sides           q+q2+3q−p=−p3p3+1−3pq+q2=0Therefore, the required condition is p3+1−3pq+q2=0