Question

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.

Answer 1

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
`x^(2) +x+ix+x+1+i-ix-i- i^(2)`. Let's put that into some order so we can see what cancels out.
`x^(2) +x+x+ix-ix+i-i+1- i^(2)`. After the canceling, we are left with
`x^(2) +2x+1- i^(2)`. Since
`i^(2) =-1`, we now have
`x^(2) +2x+1-(-1)` which of course simplifies to
`x^(2) +2x+1+1` or
`x^(2) +2x+2`. Therefore, your missing term is 2x. Phew!!!