The roots of an equation are x = -1 ± i. the equation is x2 + + 2 = 0 the blank space is where the answer should be written. this answer is not multiple choice.

Set this up to FOIL the 2 sets of factors.  They are [x-(-1+i)][x-(-1-i)] which simplify down to, after distributing the negative into each set of parenthesis: (x+1-i)(x+1+i).  FOIL these using inner first, outer last.  Doing that gives us .  Let's put that into some order so we can see what cancels out.  .  After the canceling, we are left with .  Since , we now have which of course simplifies to or .  Therefore, your missing term is 2x. Phew!!!