x^4 + 12x - 5

   = (x^2 + 2x - 1)*(x^2 - 2x + 5)

   = [x + 1 - sqrt(2)]*[x + 1 + sqrt(2)]*
     [x - 1 - 2i]*[x - 1 + 2i]

Thus, the roots are

   -1 - sqrt(2),
   -1 + sqrt(2),
    1 - 2i, and
    1 + 2i

The sum of the last two is 2.