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 + 15x^2 - 16
To find the zeros of this function, we can set the function equal to zero and solve for x:
x^4 + 15x^2 - 16 = 0
We can factor this equation using factoring by grouping:
(x^2 - 1)(x^2 + 16) = 0
Now we can set each factor equal to zero and solve for x:
x^2 - 1 = 0
x^2 = 1
x = ± √1
x = ±1
x^2 + 16 = 0
x^2 = -16
x = ± √-16
x = ±4i
Therefore, the zeros of the function are x = -1, x = 1, x = -4i, and x = 4i.