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 + 3x^2 - 4
To find the zeros of the function f(x) = x^4 + 3x^2 - 4, we need to set the function equal to zero and solve for x:
x^4 + 3x^2 - 4 = 0
We can factor this equation to make it easier to solve. First, let's substitute u = x^2:
u^2 + 3u - 4 = 0
Now we can factor this quadratic equation:
(u + 4)(u - 1) = 0
Setting each factor equal to zero gives:
u + 4 = 0 or u - 1 = 0
For u + 4 = 0, we have:
u = -4
Substituting back for u:
x^2 = -4
Taking the square root:
x = ±2i
For u - 1 = 0, we have:
u = 1
Substituting back for u:
x^2 = 1
Taking the square root:
x = ±1
Therefore, the zeros of the function f(x) = x^4 + 3x^2 - 4 are x = -2i, 2i, -1, and 1.