Question

Find the complex zeros of the following polynomial function and write F in factored form.

Answer 1

Answer:

The complex zeros are:

$\begin{gathered} x_1=-2i \\ x_2=2i \end{gathered}$

The factored polynomial is:

$f(x)=(x-1)(x-3)(x^{2}+4)$

Step-by-step explanation:

Factoring the polynomial, we'll have:

$f(x)=(x-1)(x-3)(x^2+4)$

To find the complex zeroes, let's solve for the quadratic term as following:

$\begin{gathered} x^2+4=0 \\ \rightarrow x^2=-4 \\ \rightarrow x=\pm2i \end{gathered}$