If both roots of the equation $x^{2}-(m+1)x+(m+4)=0$ are negative, then $m$ equals

For both roots of x^2 - (m+1)x + (m+4) = 0 to be negative, the sum of the roots must be less than zero, so m+1 < 0, meaning m < -1. Furthermore, the product of the roots must be positive, requiring m+4 > 0, which means m > -4. Checking the discriminant D = (m+1)^2 - 4(m+4) yields m^2 - 2m - 15, which is positive for m in the range of -4 to -1. Therefore, the values of m that satisfy all these conditions strictly fall within the range -4 < m < -1.

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