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The function \( f(x) = 9x^3 + 48x^2 + 54x + 24 \) has the following zeros:

- \( x = -4 \) (real root)
- \( x = -\frac{2}{3} - \frac{\sqrt{2}}{3}i \) (complex root)
- \( x = -\frac{2}{3} + \frac{\sqrt{2}}{3}i \) (complex root)

Since the question asks for exact values and these include complex numbers, the real root is \( x = -4 \).

Would you like more details on the solution process?

Here are 5 related questions to explore:
1. How do you solve cubic equations in general?
2. What are the differences between real and complex roots?
3. How can we factor cubic polynomials with complex roots?
4. What methods are used to graph complex roots of polynomials?
5. What role does the discriminant play in identifying complex roots?

**Tip**: To check if a cubic equation has complex roots, use the discriminant formula for cubics!

Find all zeros of f(x) = 9x^3 + 48x^2 + 54x + 24. Enter the zeros separated by commas. Enter exact value, not decimal approximations.

Learn how to find the zeros of the cubic function f(x) = 9x^3 + 48x^2 + 54x + 24. This problem explores the use of algebraic methods to solve for both real and complex roots. Suitable for students in Grades 11-12 or College Algebra.

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