I have 2 questions on the rational root theorem:

1. Can the rational root theorem be used to find all the real roots of any polynomial, assuming it has whole number coefficients? Or are there situations where there are real roots of a polynomial with whole number coefficient where some of it's real roots cannot be found through the rational root theorem? I'm asking this because my textbook says that the rational root theorem can be used to find all the real roots of any polynomial.
2. In the same textbook however, there was a question requiring you to find the real roots of $x^4+3x^2+2=0$. One of the real roots was $\pm\sqrt{2}$. How does one find this using the rational root theorem?

Please try to keep the answers at the level of a high school Pre-calc student. Thanks.