I have no idea what you mean by "do not change by squaring their roots is .....".
A quadratic equation is of the form . It has specific roots. An equation which has, as roots, those roots squared will be a different equation, necessarily.
Hmmm- on second thought, there is one possiblity. The only way to have the same equation is to have the same roots. That means that the roots of this equation must have the property that, when you square them, you get the same number again. That is, . What numbers have that property? How many quadratic equations are there having only those numbers as roots?