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 + 3x^2 - 4

Answer 1

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.