Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The roots of an equation are x = -1 ± i. The equation is x2 + + 2 = 0.

Answer 1

If those are your roots, in factorization form they are [x-(-1+i)][x-(-1-i)], which simplifies to (x+1-i)(x+1+i).  FOIL that out like you would anything else to get the mess that looks like this: $x^{2} +x+ix+x+1+i-ix-i- i^{2}$.  Putting things in order makes it easier to deal with.  $x^{2} +x+x+ix-ix+i-i+1- i^{2}$.  Canceling out what we can, gives us $x^{2} +2x+1- i^{2}$. $i^{2}=-1$.  That simplifies to $x^{2} +2x+1-(-1)$, which of course gives us $x^{2} +2x+1+1$ and $x^{2} +2x+2$ is the final result.  Your missing term there is 2x