All the values of $m$ for which both roots of the equation $\displaystyle x^{2}+2mx+m^{2}-1=0 $ are greater than $-2$ but less than $4$ lie in the interval

The roots of x^2 + 2mx + m^2 - 1 = 0 are found by factoring as (x + m - 1)(x + m + 1) = 0, giving the roots -m + 1 and -m - 1. The problem states that both roots must lie between -2 and 4, so we set up two inequalities: -2 < -m + 1 < 4 and -2 < -m - 1 < 4. Solving the first inequality yields -3 < m < 3, and solving the second inequality yields -5 < m < 1. The intersection of these two intervals is -1 < m < 3.

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