Which of the following are solutions of the equation 3 x squared plus 27 equals 0? Select all that apply.
(1 point)
Responses
negative i Start Root 3 End Root
Image with alt text: negative i Start Root 3 End Root
negative 3
Image with alt text: negative 3
negative 3 i
Image with alt text: negative 3 i
i Start Root 3 End Root
Image with alt text: i Start Root 3 End Root
3
3
3i
The solutions of the equation are:
negative i√3
negative 3
negative 3i
i√3
3
3i
To find the solutions of the equation 3x^2 + 27 = 0, we need to solve for x.
First, let's subtract 27 from both sides of the equation:
3x^2 = -27
Next, divide both sides of the equation by 3:
x^2 = -9
To find the square root of both sides, we have to consider both the positive and negative square roots:
x = ±√(-9)
Since the square root of a negative number is an imaginary number, we can rewrite -9 as -1 * 9 to simplify the equation:
x = ±√(9) * i
The square root of 9 is 3, so the solutions are:
x = -3i
x = 3i
Therefore, the correct solutions are:
negative i√3 (negative i Start Root 3 End Root)
i√3 (i Start Root 3 End Root)