The given statement is

The equation $x^2-1=0$ does not have a root lying between $0$ and $2$."

Let $y$ be a root of $x^2-1=0$ and let $y \notin (0,2)$

$\Rightarrow\:y^2-1=0$, $\Rightarrow\:y=\pm1$

$1$ lies in $(0,2)$

$\therefore$ The given statement is not true.