# Math Help - IVT

1. ## IVT

I need to show that the polynomial p(x) =x^3+2x+b, where b is any real number, has a real root by applying the Intermediate Value Theorem. Any ideas? I would greatly appreciate any help.

2. the function is continuous. lim (x-> -inf) p(x) = -inf
lim (x -> +inf) p(x) = +inf

therefore by the intermediate value thm the function hits all values between -inf and +inf, including zero

something like that i think

3. When you say inf, I assume you mean infimum? How does that help? I don't mean to sound unappreciative, I'm just not making the connection.

4. inf ... infinity

5. ahhh... I'm an idiot . Makes much more sense now. Thanks a lot for the help!