I'd be happy to help you with the problem and provide a step-by-step explanation.
To find the roots of the quadratic equation -3x^2 - 8, we can use the quadratic formula. The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a, b, and c correspond to the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
For our quadratic equation -3x^2 - 8, we have:
a = -3
b = 0 (since there is no x term)
c = -8
Plugging these values into the quadratic formula, we get:
x = (-0 ± √((0)^2 - 4(-3)(-8))) / (2(-3))
Simplifying further:
x = ± √(0 - 96) / -6
x = ± √(-96) / -6
Now, we can simplify the square root of -96. Taking the square root of a negative number gives us an imaginary number. In this case, the square root of -96 simplifies to 4i√6.
Finally, we can write the roots as:
x = 2i√6 / -3 and x = 2i√6 / 3
So, the roots of the quadratic equation -3x^2 - 8 are 2i√6 / -3 and 2i√6 / 3.
I hope that helps! Let me know if you have any more questions or if there's anything else I can assist you with.