How to find the amount of irrational roots just based on knowing the amount of rational and real roots in a polynomial?

Question

If i know the amount of of rational roots in a polynomial and the amount of real roots in a polynomial. Can subtract the amount of rational roots in from the amount of Real roots in the polynomial to get the amount of irrational roots in a polynomial?

Answer 1

Yes, you can do that since real numbers contain only rational and irrational numbers. So you CAN subtract the number of rational roots from the number of real roots, to get the number of irrational roots. But there is no guarantee that they will be algebraic.