Question

What are the solutions of the quadratic equation \(3x^2 - 6x + 6 = 0\)?

a) \(-2 \pm i\)
b) \(-2 \pm 2i\)
c) \(-1 \pm i\)
d) \(1 \pm i\)

Select the correct solutions for the given quadratic equation.

Answer 1

To find the solutions to the quadratic equation 3x^2 - 6x + 6 = 0, we can use the quadratic formula. The equation has no real solutions, but the correct answer is Option A) -2 ± i.

Step-by-step explanation:

To find the solutions to the quadratic equation 3x^2 - 6x + 6 = 0, we can use the quadratic formula. For an equation of the form ax² + bx + c = 0, the solutions are given by the formula x = (-b ± √(b² - 4ac)) / (2a).

Substituting the values a = 3, b = -6, and c = 6, we get x = (-(-6) ± √((-6)² - 4(3)(6))) / (2(3)). Simplifying this gives us x = (6 ± √(36 - 72)) / 6, which further simplifies to x = (6 ± √(-36)) / 6.

Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, the correct answer is Option A) -2 ± i (where i represents the imaginary unit).