Question

If a polynomial function f(x) has roots 4 – 13i and 5, what must be a factor of f(x)?

(x + (13 – 4i))

(x – (13 + 4i))

(x + (4 + 13i))

(x – (4 + 13i

Answer 1

The answer should be D

Answer 2

factor is (x-(4-13i))

Explanation:

If a polynomial function f(x) has roots 4 – 13i and 5

One of the complex root is 4-13i

If we have one complex root then there should be one more complex root

complex roots are come in pairs like (a+ib) and (a-ib)

so another complex root for 4-13i is 4+13i

If 'a' is a root then factor is (x-a)

4+13i is a root

so factor is (x-(4-13i))