Final answer:
The equation has 0 zeros.
Step-by-step explanation:
To find the number of zeros for the equation F(x) = -(x-7)^2 - 8, we set the equation equal to zero:
-(x-7)^2 - 8 = 0
However, since the equation is in the form of a negative square of a binomial minus a constant, and the square of a binomial is always non-negative, we know the function will always be negative or zero and will not intersect the x-axis. Next, we can solve this equation by isolating the squared term and taking the square root on both sides:
(x-7)^2 = -8
x-7 = ±√(-8)
Since we cannot take the square root of a negative number in the real number system, there are 0 zeros for the equation.