Question

If 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

1) one-ninth i
2) -9i
3) 9 - i
4) negative one-ninth i

Answer 1

The root -9i must also be a root of f(x).

Step-by-step explanation:

The given polynomial function is f(x), and we know that 9i is a root of f(x). To find which of the given options must also be a root of f(x), we can use the conjugate property of complex roots. The conjugate of a complex number a+bi is a-bi.

So, the conjugate of 9i is -9i. Therefore, -9i must also be a root of f(x) (Option 2).