Answer:To solve the equation 3x^2 + 2 = 0, we need to find the values of x that make the equation true.
Let's solve the equation step by step:
1. Start with the equation: 3x^2 + 2 = 0
2. Subtract 2 from both sides of the equation to isolate the quadratic term: 3x^2 = -2
3. Divide both sides of the equation by 3 to solve for x^2: x^2 = -2/3
Now, we have an equation for x^2. To find the solutions for x, we need to consider the square root of both sides of the equation. However, it's important to note that the square root of a negative number is not a real number, but an imaginary number. In this case, we need to use the imaginary unit "i" to represent the square root of -1.
4. Take the square root of both sides: x = ±√(-2/3)
Since we are looking for the solutions to the equation, we need to consider both the positive and negative square root of -2/3.
5. Simplify the square root: x = ±(√(2/3)i)
Therefore, the solutions to the equation 3x^2 + 2 = 0 are x = (√(2/3)i) and x = -(√(2/3)i).
To summarize, the correct answer is (√6/3)i.
Explanation: