= Root bracket
{title2=$[a,b]$}
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>.
Back to article page
