Since sum of the roots is negative and product of the roots is positive.
So, both roots are negative
Thus m is a negative root
Now, tan-1(m) + tan-1(1/m)
= tan-1(m) - π + cot-1(m)
= - π + (tan-1(m) + cot-1(m))
= - π + π/2 = - π/2
Clearly, k = -1
Hence, the value of (k + 4) is 3.