Intermediate Value Theorem/Corollary

Theorem
Let $I$ be a real interval.

Let $a, b \in I$ such that $\openint a b$ is an open interval.

Let $f: I \to \R$ be a real function which is continuous on $\openint a b$. Let $0 \in \R$ lie between $\map f a$ and $\map f b$.

That is, either:
 * $\map f a < 0 < \map f b$

or:
 * $\map f b < 0 < \map f a$

Then $f$ has a root in $\openint a b$.

Proof
Follows directly from the Intermediate Value Theorem and from the definition of root.