Question

Using the given zero, find all other zeros of f(x). -2i is a zero of f(x) = x4 - 21x2 - 100

Answer 1

To find the other zeros of the function f(x) = x^4 - 21x^2 - 100 given that -2i is a zero, we can use the conjugate zero theorem.

Since -2i is a zero, its conjugate 2i will also be a zero of the function.

Now we can use polynomial long division or synthetic division to find the quadratic expression that results from dividing f(x) by (x + 2i)(x - 2i).

Performing the division, we get:

(x^4 - 21x^2 - 100) / ((x + 2i)(x - 2i)) = x^2 - 5

So the other two zeros of f(x) are the solutions to the equation x^2 - 5 = 0.

Solving this equation, we find two additional zeros: x = √5 and x = -√5.

Therefore, the zeros of the function f(x) = x^4 - 21x^2 - 100 are -2i, 2i, √5, and -√5.