What does the degree of a polynomial have to do with the finite extension of a body?

Question

Let L : K be a finite extension, and let p be an irreducible polynomial over K. Show that if op and [L : K] are coprime, .then p has no zeros in L .

Answer 1

Assuming by "op" you mean deg($p$) (maybe this is notation I'm unfamiliar with) assume $\theta \in L$ is a root of $p$ and consider the field tower $K \subset K(\theta) \subset L$, can you get a contradiction based on the degrees of these extensions ?