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,thoseroots squared will be adifferentequation, necessarily.

Hmmm- on second thought, there is one possiblity. The only way to have thesameequation is to have thesameroots. 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 havingonlythose numbers as roots?