Question

F(x) = x^3 + 9x

Find the zeros and imaginary zeros.

a. Zeros: x = 0, Imaginary zeros: None
b. Zeros: x = 0, Imaginary zeros: x = ±3i
c. Zeros: x = ±3, Imaginary zeros: x = 0
d. Zeros: x = 0, Imaginary zeros: x = ±3

Answer 1

The function f(x) = x^3 + 9x has one real zero at x = 0 and two imaginary zeros at x = ±3i, which means the correct answer is b. Zeros: x = 0, Imaginary zeros: x = ±3i.

Step-by-step explanation:

To find the zeros and imaginary zeros of the function f(x) = x^3 + 9x, we will first factor out what's common, which is x. This gives us:

f(x) = x(x^2 + 9)

We can easily see that x = 0 is a zero of the function. We then set the other factor equal to zero to find the remaining zeros:

x^2 + 9 = 0

Solving for x, we get:

x^2 = -9

x = ±√(-9)

x = ±3i

Therefore, we have one real zero at x = 0 and two imaginary zeros at x = ±3i.

So the correct answer is b. Zeros: x = 0, Imaginary zeros: x = ±3i.