Answer:
x^2 - 4x + 5 = 0.
Step-by-step explanation:
Note that the roots of (x - b)( x - c) = 0 are b and c, so:
We write it in factor form
(x - (2 + i)(x - (2 - i) = 0
Now expand:
x^2 - x(2 - i) - x(2 + i) -(2 + i)* - (2 - i) = 0
x^2 - 2x + ix - 2x - ix + (4 - 2i +2i - i^2)
x^2 - 4x + 4 + 1 = 0
x^2 - 4x + 5 = 0 (answer).
