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

Which of the following is a root of the polynomial function below? F(x)=x^3+3x^2+4x-example-1
User Chobo
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8.4k points

1 Answer

1 vote

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

Which of the following is a root of the polynomial function below? F(x)=x^3+3x^2+4x-example-1
User Jake Braun
by
7.6k points

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