$x^2-2mx+m^2-1=0$ Find the range of m when one root lies in (-2, 4) Let: $x^2-2mx+m^2-1=0$. For all $m$ there exist real roots for the above equation. If one root lies in between $(-2,4)$ Find the value range for $m$

My Work

Since coefficient of $x^2$ is 1 the graph is a maximum. Also the discriminant is positive. How can I use this fact to solve this problem ? Please Help me. Thanks a lot
$$1=(x-m)^2\iff x=m\pm1$$

Check for

$2&lt;m-1&lt;4$

and $2&lt;m+1&lt;4$
The roots are $m+1$ or $m-1.$ Since one of them must stay within $(-2,4),$ we must have $-2&lt;m+1&lt;4,$ or $-2&lt;m-1&lt;4,$ which give $-3&lt;m&lt;3,$ or $-1&lt;m&lt;5.$ Thus, $m$ must satisfy the conditions $$-3&lt;m&lt;5.$$