Question

Homework17. What are all the real and complex zeros ofthe polynomial function shown in the graph?SEE EXAMPLE 3ty84I-4 -2O24ANf(x) = x3 x2 - 4x - 6

Answer 1

Given:

`f(x)=x^3-x^2-4x-6`

When x=3,

`\begin{gathered} f(3)=3^3-3^2-4(3)-6 \\ f(3)=27-9-12-6 \\ f(3)=0 \end{gathered}`

(x-3) is a factor of f(x).

`f(x)=(x-3)(x^2+2x+2)`
`\begin{gathered} x=\frac{-2\pm\sqrt[]{4-4(1)(2)}}{2} \\ x=\frac{-2\pm\sqrt[]{4-8}}{2} \\ x=\frac{-2\pm\sqrt[]{-4}}{2} \\ x=-1\pm i \end{gathered}`

Therefore the values of x are:

`x=3,-1+i,-1-i`