Write the simplest polinomial function with this zeros: √5, 2√2, -3

To write the simplest polynomial function with the given zeros \(\sqrt{5}\), \(2\sqrt{2}\), y \(-3\), we use the fact that if a polynomial has roots \(r_1\), \(r_2\), and \(r_3\), then the polynomial can be expressed as:

\[
f(x) = a(x - r_1)(x - r_2)(x - r_3)
\]

For the simplest polynomial (where \(a = 1\)), we substitute the given roots:

\[
f(x) = (x - \sqrt{5})(x - 2\sqrt{2})(x + 3)
\]

This is the simplest polynomial function with the given zeros.

Would you like to expand this polynomial, or do you have any other questions?

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### Related Questions:
1. How do you find the roots of a polynomial function?
2. What does it mean for a polynomial to have a certain zero?
3. Can a polynomial have irrational or complex roots?
4. How do you write a polynomial function if the roots are complex?
5. What is the degree of the polynomial with three given roots?
6. How do you determine the multiplicity of a root in a polynomial?
7. What is the relationship between the roots and the factors of a polynomial?
8. How can you verify that a given number is a root of a polynomial?

**Tip:** Remember that the degree of a polynomial is determined by the highest power of \(x\) when expanded.

Learn how to write the simplest polynomial function with zeros √5, 2√2, and -3. Understand the method of using roots to form a polynomial expression. Suitable for advanced high school students (Grades 10-12).

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