Chapter 4.6, Problem 20E

To determine

To find: the number of imaginary zeros for the function with the given degree and graph.

Answer to Problem 20E

The equation must have 3 zeros.

The numbers of imaginary zeros are 0.

Explanation of Solution

Given information:

Given degree: 3

Given graph:

  

Calculation:

The fundamental theorem of algebra states that “if $f\left(x\right)$ is degree of polynomial $n$ where $n>0$ , then the equation $f\left(x\right)=0$ has exactly $n$ solutions”.

Because the degree of function is 3, so the equation must have 3 zeros.

From the graph it is very clear that the graph crosses $x$ axis three points. So, there are three real zeros.

Therefore, the numbers of imaginary zeros are,

  $3-3=0$

So, the numbers of imaginary zeros are 0.