Root bracket ($[a,b]$)

A root bracket is a closed interval known to contain at least one zero of a function. For a real-valued continuous function on $[a,b]$, a strict change of sign between $f(a)$ and $f(b)$ certifies such an enclosure by the intermediate value theorem. An endpoint with value zero already supplies a zero of a function. For example, $[1,2]$ is a root bracket for the polynomial $f(x)=x^2-2$, since $f(1)=-1$ and $f(2)=2$. A root bracket need not contain a unique zero of a function.