Final answer:
The equation with solutions x = -3 ± √ 3 i is x² + 6x + 9 = 0. By using the quadratic formula, we can see that the discriminant is zero, which is consistent with the given complex roots.
Step-by-step explanation:
The solutions x = - 3 ± √ 3 i suggest we are dealing with a quadratic equation with complex roots. By the structure of the solutions, we can discern that the equation must feature a perfect square and result in complex conjugate roots. When we look at the solutions, we can see that the middle term of the quadratic should be positive to yield a negative real part of the solutions. Therefore, the correct equation that fits these criteria is x² + 6x + 9 = 0.
To verify this, we can use the quadratic formula -b ± √(b² - 4ac)/2a. Plugging the coefficients a = 1, b = 6, and c = 9 into the formula, we find that the discriminant (b² - 4ac) is zero, which indicates that the roots are a pair of complex conjugates with real parts equal to -b/2a and imaginary parts related to the square root of the negative discriminant, confirming our initial given solutions.