Properties of Continuous Functions

[bearej50]

Show that any polynomial of odd degree has at least one real root.

I think that I would use the intermediate value theorem... but how?

 

[daon]

Odd degree polynomials ultimately tend to negative infinity in one direction and positive infinity in the other.

Show there exists a point a such that p(a)>0 and another point b such that p(b) < 0. Then apply the intermediate value theorem.