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

A function f : R → R defined as f(x) = a_{n} x^{n} + a_{n − 1} x^{n − 1} + … + a_{2} x^{2} + a_{1} x + a_{0} is called a polynomial function in variable x. where, a_{0}, a_{1},…, a_{n} are real number constants and n is a non-negative integer.

## Answer: If a polynomial function f(x) has roots (4 – 13i) and 5, then [x - (4 - 13i)] or (x - 5) must be a factor of f(x).

Let's see in detail.

**Explanation:**

Given,

The roots of the polynomial function f(x) are (4 - 13i), and 5

If 'a' is a root of the polynomial function f(x) then the factor is (x - a)

Hence factors of the polynomial can be formed as [x - (4 - 13i)] and (x - 5)