What are the roots of this equation? x2 − 2x + 3 = 0

C

one way to solve is to use the method of completing the square

subtract 3 from both sides

x² - 2x = - 3

add ( half the coefficient of the x-term )² to both sides

x² + 2(- 1 )x + 1 = - 3 + 1

(x - 1)² = - 2

take the square root of both sides

x - 1 = ± √(- 2) = ± i√2 ( add 1 to both sides )

x = 1 ± i√2 → C