Proof that there are (one variable) polynomials of any natural degree with rational coefficients, which are irreducible over the field of rational numbers.
Proof that there are (one variable) polynomials of any natural degree with rational coefficients, which are irreducible over the field of rational numbers.
Thanks.
In other words, show that, given any n> 0, there exist a polynomial of degree n which has no rational root.
I would suggest looking at $\displaystyle x^n- p= 0$ where p is a prime number.