Also note that in your field reduces to just .
Just to make sure I get it right.
is a field.
We want to express as a polynomial of degree less than 2.
Also, I have to find the roots of
but 2 is not a perfect square in
has no root.
Is that right????
But reduce to 1 only if t=x. Therefore there might be roots even if x is not a root. For example, in this field, has two roots that are x and -x.
Yes it's a cheap example but it's late and it still gives the idea. x is not a variable anymore in this field. 'Polynomials' becomes roots.
Anyway, good night.