Question

The roots of an equation are x = -1 ± i. The equation is x2 +__ + 2 = 0.

Answer 1

[x-(-1+i)][x-(-1-i)]
[(x+1)-i][(x+1)+i]
(x+1)²-i²
(x²+2x+1)+1
x²+2x+2
so the answer is 2x

Answer 2

Answer:

The Roots of the equation which is in Quadratic form  are:

    $x= -1 \pm i\\\\ x +1=\pm i\\\\ \text{Squaring both sides}}\\\\ (x+1)^2=(\pm i)^2\\\\ x^2 +2 x +1= -1\\\\x^2+2 x +2=0$

The Equation is

 x²+2 x +2=0