Question

Which of the following is a root of the polynomial function below? F(x)= x+3x? -5x - 4 Ο Α. 4 O O 2 2 o B. 1 B 1 O c. 1.5 Ос 3 3 OD 3 D. 3

Answer 1

Given:

`f(x)=x^3+3x^2-5x-4`

To determine the roots, we let f(x)=0 first:

`x^3+3x^2-5x-4=0`

Next, we find factor of the equation:

`\begin{gathered} x^3+3x^2-5x-4=(x+4)(x^2-x-1)=0 \\ \end{gathered}`

Then, we use quadratic formula for x^2-x-1=0:

We plug in what we know:

Hence,

We also get the x value of x+4=0:

`\begin{gathered} x+4=0 \\ x=-4 \end{gathered}`

Therefore, the answer is: