The graph you have provided represents a 5th-degree polynomial function. Based on the Fundamental Theorem of Algebra, we know that a polynomial of degree $n$ has exactly $n$ complex roots (including real and imaginary zeros).

Analyzing the graph:

• Real zeros are where the graph crosses the x-axis. From the graph, we can see that the polynomial crosses the x-axis once.

  • Therefore, there is 1 real zero.

• The total number of zeros (real and imaginary) must add up to 5 since it's a 5th-degree polynomial.

  • Since there is 1 real zero, the remaining $5 - 1 = 4$ zeros must be imaginary.

Conclusion:

• Number of real zeros: 1
• Number of imaginary zeros: 4

Would you like a more detailed explanation of this concept? Also, here are some related questions to explore further:

1. What is the Fundamental Theorem of Algebra?
2. How do we determine if a polynomial has imaginary roots by looking at the graph?
3. Why do imaginary zeros always come in pairs for polynomials with real coefficients?
4. Can a polynomial of odd degree have only imaginary roots?
5. How can we factor a polynomial to identify its real and imaginary zeros?

Tip: Remember, imaginary roots always occur in conjugate pairs, so the number of imaginary zeros in a polynomial with real coefficients will always be an even number!