Find all the zeros of the following function.
(Use a comma to separate answers as needed. Express complex numbers in terms of i.)
f(x) = x^4 - 8^2 - 9
To find the zeros of the function, we set f(x) equal to zero and solve for x.
x^4 - 8^2 - 9 = 0
x^4 - 64 - 9 = 0
x^4 - 73 = 0
To solve this equation, we can try factoring or using the quadratic formula.
Unfortunately, this equation cannot be factored easily. So, we will use the quadratic formula to solve for x^2.
Let's substitute y = x^2:
y^2 - 73 = 0
y^2 = 73
y = ±√73
Now, we substitute back for x^2:
x^2 = ±√73
x = ±√(±√73)
Therefore, the zeros of the function f(x) = x^4 - 64 - 9 are:
x = ±√(±√73)