Answer:
If the roots of a quadratic equation are given as x = -1 ± 2i, then the equation can be written in the form:
(x - (-1 + 2i))(x - (-1 - 2i)) = 0
Simplifying this expression, we get:
(x + 1 - 2i)(x + 1 + 2i) = 0
Expanding the left side of this equation, we get:
x^2 + x(2 - 2i + 2 + 2i) + (1 - 2i)(1 + 2i) = 0
Simplifying this expression, we get:
x^2 + 2x + 5 = 0
Therefore, the quadratic equation with roots of x = -1 ± 2i is:
x^2 + 2x + 5 = 0