Which of the following are solutions of the equation 3 x squared plus 27 equals 0?

Question

(1 point)
ONLY TWO AWNSERS!!!!!
Responses

negative i Start Root 3 End Root
- image with description: negative i Start Root 3 End Root - - only 2 answers are allowed

-3

-3i

i Start Root 3 End Root
- image with description: i Start Root 3 End Root - - only 2 answers are allowed

3

3i

Answer 1

To solve the equation \( 3x^2 + 27 = 0 \), we first simplify it:

1. Subtract 27 from both sides: \[ 3x^2 = -27 \]

2. Divide both sides by 3: \[ x^2 = -9 \]

3. Now, take the square root of both sides: \[ x = \pm \sqrt{-9} \]

4. Since \(\sqrt{-1} = i\) and \(\sqrt{9} = 3\), we get: \[ x = \pm 3i \]

Thus, the solutions of the equation \( 3x^2 + 27 = 0 \) are \( 3i \) and \( -3i \).

From the responses provided, the correct answers are:

• \( -3i \)
• \( 3i \)