Final answer:
To find the equation of the polynomial function, we use the zeros and y-intercept. Given the zeros x = 2 + 4i and x = 3, and the y-intercept at (0, -60), we can write the equation. The polynomial function will have a degree of 3 and real coefficients.
Step-by-step explanation:
To determine the equation of a polynomial function with degree 3 and real coefficients, we need to find its zeros and the y-intercept. Given that the zeros are at x = 2 + 4i and x = 3, and the y-intercept is at (0, -60), we can write the equation as:
f(x) = a(x - 2 - 4i)(x - 2 + 4i)(x - 3)
Since the coefficients are real, the complex conjugate zeros occur in pairs. Therefore, the equation can be simplified as:
f(x) = a(x - (2 - 4i))(x - (2 + 4i))(x - 3)
Expanding this equation will give us a polynomial function of degree 3 with real coefficients.