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 + 15x^2 - 16

Answer 1

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.