Question

Which of the following is a root of the polynomial function below? F(x)=x^3+3x^2+4x+12

Answer 1

Step-by-step explanation

We are asked to select the root of the equation for the function

`f(x)=x^3+3x^2+4x+12`

The first step will be to get the factor

So that

`f(x)=(x+3)(x^2+4)`

so that

`\begin{gathered} x+3=0\text{ is a root} \\ x=-3\text{ is a root} \end{gathered}`

Next, we will simplify further by getting the zeros of x²+4

Thus

`\begin{gathered} x^2=-4 \\ \\ x=√(-4) \\ \\ x=\pm2i \end{gathered}`

So we can see that the factors of x²+4 are imaginary roots (2i and -2i)

Hence, the root of the given polynomial are:

`-3,2i,\text{ and -2i}`

Hence, the correct answer is option D