let k be the constant .If a and b are the roots of the equation x^2+4x-k=0 , then 4a-b^2=

x^2+4x-k=0

One root is  [ -4 +√(16 + 4k)]/2  = [-2 + √(4 + k)]

And the other is just  [-2 - √(4 + k)]

And let a be the first root and b, the second...so 4a - b^2 =

4[-2 + √(4 + k)] - [-2 - √(4 + k)]^2 =

-8 + 4√(4 + k) - [ 4 + 4√(4 + k) + 4 + k ] =

-8 + 4√(4 + k) - 4 - 4√(4 + k) - 4 - k =

-16 - k

BTW.....the result is the same if we "swap" the roots....!!!