Question was to find the roots whose roots are square of the given roots of this polynomial $x^{3}+a x^{2}+b x+c=0$
I did used tranformation method to obtain $y^{3 / 2}+a y+b y^{\frac{1}{2}}+c=0$ but as we want to have to get a three degree equation only so we need to simplify the above carefully , one way would be to square just the y^3/2 term and the rest on the other side , but that will leave a radical on y again , so we have to again square it to get a 6th degree equation ,but when we simplify by squaring with y^3/2 and y^1/2 terms on one side it pretty easily givea the 3degree equation we wanted. My doubt is what happened with the 6th degree equation what extra 3 roots are from ? Are they same roots ?