https://file.aiquickdraw.com/mathbot/file/1733951415706oavtrvoc.jpg

To find a polynomial \( f(x) \) of degree 4 that has the specified zeros, we use the fact that a polynomial's zeros correspond to its factors. If the given zeros are \(-1\), \(-3\), \(4\), and \(7\), the polynomial in factored form is constructed as:

\[
f(x) = (x + 1)(x + 3)(x - 4)(x - 7)
\]

This is the solution in factored form. Do you need me to expand it, or provide further details?

---

### Relative Questions:
1. How do you verify that these are indeed the zeros of the polynomial?
2. What happens if one or more of the zeros has a multiplicity greater than 1?
3. How does this approach change if the polynomial is required to include a leading coefficient other than 1?
4. Can you expand this polynomial and confirm that it is a degree 4 polynomial?
5. What if one of the zeros is complex? How do we handle such a situation?

---

### Tip:
Always check if the polynomial needs a specific leading coefficient or constant term to ensure it satisfies all given conditions.

Find a polynomial f(x) of degree 4 that has the following zeros: -1, -3, 4, 7. Leave your answer in factored form.

Learn how to construct a degree 4 polynomial with given zeros: -1, -3, 4, and 7. The solution is provided in factored form, suitable for high school students in Grades 10-12 studying polynomials and algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation