Question

1f-3+i is a √ of the polynomial function f(x), which of the following must also be a √ of f(x)?

a) 0 - 3 - 1
b) 0 - 3i - 1i
c) 0 3 - 1
d) 3i - 3 - 1

Answer 1

To find which option is also a root of f(x), we can use the conjugate root theorem. The correct answer is option (a) 0 - 3 - 1.

Step-by-step explanation:

In this question, we are given that 1f-3+i is a √ of the polynomial function f(x). We need to determine which of the given options must also be a √ of f(x).

To solve this, we need to use the conjugate root theorem. According to this theorem, if a+bi is a root of a polynomial with real coefficients, then its conjugate a-bi is also a root.

Applying the theorem, since 1f-3+i is a root of f(x), its conjugate 1f-3-i must also be a root. Therefore, the correct answer is option (a) 0 - 3 - 1.