Question

Use the given zero to find the remaining zeros of the function.

Answer 1

The remaining zeros are -7i, 4

Explanations:

Given the polynomial function:

`f(x)=x^3-4x^2+49x-196`

Group the functions:

`f(x)=(x^3-4x^2)+(49x-196)`

Factor out the common term in both parenthesis

`\begin{gathered} f(x)=x^2(x-4)+49(x-4) \\ f(x)=(x^2+49)(x-4) \end{gathered}`

Get the zeros of the function by making f(x) = 0

`\begin{gathered} (x^2+49)(x-4)=0 \\ \end{gathered}`

Equate both factors to zero;

`\begin{gathered} x^2+49=0 \\ x^2=-49 \\ x=\pm\sqrt[]{-49} \\ x=\pm\sqrt[]{49}*\sqrt[]{-1} \\ x=\pm7i \end{gathered}`

For the other factor (x-4) = 0

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

Given one of the zeros as 7i, the other zeros of the function will be -7i and 4