>>13137319>then X^2 will be a zero of P^2.This is obviously not true. P^2 has the same zeros as P.
>>13133537There are two ways to show this. By some basic theory, finite extensions of fields are algebraic, so if you have some algebraic numbers x1,x2,x3...xn , anything you can build out of them and Q by adding/multiplying/dividing is also algebraic.
There's also a trick you can use. Take a primitive kth root of unity , and any polynomial f. Then you have for some p. The roots of p are exactly the kth powers of the roots of f.
