Final answer:
To find the zeros of the function r(x) = -1/2x² - 24, set the function equal to zero and solve for x. Since the square root of a negative number is not defined in the real number system, this function has no real zeros.
Step-by-step explanation:
To find the zeros of the function r(x) = -1/2x² - 24, we need to set the function equal to zero and solve for x. So we have:
-1/2x² - 24 = 0
Adding 24 to both sides gives us:
-1/2x² = 24
Now, multiplying both sides by -2 to eliminate the fraction, we get:
x² = -48
Taking the square root of both sides, we have:
x = ±sqrt(-48)
Since the square root of a negative number is not defined in the real number system, this function has no real zeros.