Find all the zeros of the following function.

Question

(Use a comma to separate answers as needed. Express complex numbers in terms of ​i.)

f(x) = x^4 - 8^2 - 9

Answer 1

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)