Question

Solve the equation by using the Quadratic Formula.

3⁢𝑥^2−6⁢𝑥+11=0

Simplify your solutions. If the solutions are real rational numbers, list from least to greatest separated by a comma. If the solutions are not real numbers, write your answer in the form a ± bi. If the solutions are irrational, write your answer in simplified radical form, using ± to express both solutions.

Answer 1

Use the quadratic formula x = [-b ± sqrt(b^2 - 4ac)]/(2a) with a=3, b=-6, c=11.

b^2 - 4ac = (-6)^2 - 4(3)(11) = 36 - 132 = -96.
sqrt(-96) = 4i sqrt(6).

x = [6 ± 4i sqrt(6)]/6 = 1 ± (2/3)i sqrt(6).

So the solutions are 1 ± (2√6/3) i.