if a polynomial function f(x) has roots 4 - 13i and 5, what must be a factor of f(x)?\n(x + (13 - 4i))\n(x…

if a polynomial function f(x) has roots 4 - 13i and 5, what must be a factor of f(x)?\n(x + (13 - 4i))\n(x - (13 + 4i))\n(x + (4 + 13i))\n(x - (4 + 13i))

if a polynomial function f(x) has roots 4 - 13i and 5, what must be a factor of f(x)?\n(x + (13 - 4i))\n(x - (13 + 4i))\n(x + (4 + 13i))\n(x - (4 + 13i))

Answer

Answer:

D. $(x-(4 - 13i))$

Explanation:

Step1: Recall factor - root relationship

If $r$ is a root of a polynomial function $f(x)$, then $(x - r)$ is a factor of $f(x)$.

Step2: Identify given roots

The roots are $r_1=4 - 13i$ and $r_2 = 5$.

Step3: Determine factors

For root $r_1=4 - 13i$, the factor is $(x-(4 - 13i))$; for root $r_2 = 5$, the factor is $(x - 5)$. Among the given options, the correct factor corresponding to the root $4-13i$ is $(x-(4 - 13i))$.