Final answer:
The solutions to the quadratic equation 3x^2 + 2 = 0 are x = (√(6) / 3)i and x = -(√(6) / 3)i, which are complex numbers due to the presence of the imaginary unit 'i'.
option a is the correct
Step-by-step explanation:
The student is asking how to find the solution to the quadratic equation 3x2 + 2 = 0. This type of problem is commonly solved using the quadratic formula, x = (-b ± √(b2 - 4ac)) / (2a). Applying this formula to the given equation, we substitute the coefficients a = 3, b = 0 (since there is no x term), and c = 2.
Upon substituting, we have:
x = (0 ± √(02 - 4×3×2)) / (2×3)
x = ±√(-24) / 6
x = ±√(-1)√(24) / 6
Since the square root of a negative number is an imaginary number, the solution will be in terms of 'i', where i = √(-1). Therefore, x = ±(√(24) / 6)i. Simplifying √(24) as 2√(6) gives us x = ±(2√(6) / 6)i or x = ±(√(6) / 3)i.
The correct solution is therefore x = (√(6) / 3)i and x = -(√(6) / 3)i, not the options provided in the original question. Thus, (2/3)i is not a correct solution to the equation 3x2 + 2 = 0.