Bolzano's Root Point Theorem

analysis

Definition

Bolzano's Root Point Theorem

Let $f:[a,b]\to \mathbb{R}$ be a continuous function with $f(a)\cdot f(b)<0$. Then $f$ has at least one root in the open interval $(a,b)$: there exists $c\in (a,b)$ such that $f(c)=0$.

It is the special case of the Intermediate Value Theorem in which the intermediate value is $0$.