1. (1) Find all of the zeros of f.
Students, Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary.
Use the function below to answer the questions.
(1) Find all of the zeros of f.

2. THE QUADRATIC FORMULA: works on all quadratics
where
Use the quadratic formula.
a = 2, b = -1, c = -6

3. Fundamental Theorem of Algebra
If f(x) is a polynomial of degree n, where n > 0, then f has at least one zero in the complex number system.
Linear Factorization Theorem
If f(x) is a polynomial of degree n, where n > 0, then f has precisely n linear factors

4. 3) Write the function as a product of its linear factors, and list all the zeros of f.

5. 1) Counting multiplicity, confirm that the second-degree polynomial function has exactly two zeros.
2) Confirm that the third-degree polynomial function has exactly three zeros.

6. Complex zeros occur in pairs
If a + bi is a zero, then so is a – bi
Ex 1) Find a fourth-degree polynomial function with real coefficients that has – 2, – 2, and 3 + i as zeros.

7. Ex 2) Find all the zeros of f(x) given that 2 – 2i is a zero of f.

8. 4) Write as a product of linear factors:
5) Find a third-degree polynomial with integer coefficients that has 2 and 3 – i as zeros.