If the equation whose roots are the squares of the roots of the cubic is identical with the given cubic equation, then
Given equation is . If roots of the equation be , then
So, the equation whose roots are is given by
It is identical to
Eliminating b, we get
which gives b = 0 or b = 3 or b2 + b + 2 = 0. So, a = b = 0 or a = b = 3 or a, b are roots of x2 + x + 2 = 0.