Question

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

Answer 1

x² + 2x + 2 = 0

Explanation:

Given that the roots are x = - 1 + i and x = - 1 - i

Then the factors are

(x - (- 1+ i))(x - (- 1 - i)

= (x + 1 - i)(x + 1 + i) ← expand factors

= (x + 1)² - i² → note i² = - 1

= x² + 2x + 1 + 1

= x² + 2x + 2

Equation is x² + 2x + 2 = 0