Question

Solve 𝑥2−6⁢𝑥+21=0 by using the Quadratic Formula.

Multiple choice question.

A)
3 ±𝑖⁢√3


B)
3±2⁢𝑖⁢√3


C)
3 ±2⁢√3


D)
2 ±2⁢𝑖⁢√3

Answer 1

Use the quadratic formula x = [-b ± √(b^2 − 4ac)]/(2a) with a=1, b=−6, c=21:

Discriminant = (−6)^2 − 4(1)(21) = 36 − 84 = −48.
x = [6 ± √(−48)]/2 = [6 ± 4i√3]/2 = 3 ± 2i√3.

Answer: B) 3 ± 2 i √3.