Question

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

Answer 1

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)`

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}`