set of all $2\times 2$ matrcies having neither eigen value is real

Question

Could any one tell me whether the following subsets of $M_2(\mathbb{R})$ are open, closed or neither open nor closed?

1. set of all $2\times 2$ matrcies having neither eigen value is real.

2. set of all $2\times 2$ matrcies having oth eigen value is real.

Thanks for helping I have no idea how to proceed just from the knowledge of eigen values to know such subsets are closed or open or etc.

Answer 1

Consider the characteristic polynomial $f$ of a generic matrix $A$. The coefficients of $f$ are polynomials in the entries of $A$. Now how do you express your conditions defining the two sets in terms of the coefficients of $f$?