The sum of irrationals does not always equal a rational.does always the sum of two not rational numbers is a not rational number?
They're both irrational but which is rational.
As for your problem, you found out through the rational root theorem that the only possible rational roots are: .
If you plugged them in, they are not roots to your quadratic and so there are no rational roots, i.e. is not rational. This leads to your contradiction.