#### Answer

The graph is shown below:

#### Work Step by Step

The polynomial function is, $f\left( x \right)=3{{x}^{4}}+4{{x}^{3}}-7{{x}^{2}}-2x-3$
The degree of the polynomial function is $4$.
From the above graph it can be seen that the function $f\left( x \right)$ cut the horizontal axis $\left( x-\text{axis} \right)$ at two points. That means the number of real roots of the function is $2$.
The number of imaginary roots of the function is equal to the difference between the degree of the function and the number of real roots.
Therefore, the number of imaginary root is,
$\begin{align}
& \left( \text{degree}\text{of}\ \text{the}\ \text{function} \right)-\left( \text{number}\ \text{of}\ \text{real}\ \text{root} \right)=4-2 \\
& =2
\end{align}$