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# Ca8e Ppt 5 6

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### Ca8e Ppt 5 6

1. 1. Section 5.6<br />Complex Zeros;<br />Fundamental Theorem of Algebra<br />
2. 2.
3. 3.
4. 4.
5. 5.
6. 6. Example 1<br />A polynomial of degree 5 whose coefficients are real numbers has the zeros -2, -3i, and 2+4i. Find the remaining two zeros.<br />
7. 7. By the conjugate pairs theorem, if x = -3i and x = 2+4i <br />then x = 3i and x = 2-4i<br />
8. 8. Example 2: Find the remaining zeros of f.<br />Degree 5; zeros: 1, i, 2i<br />The degree indicates the number of zeros a polynomial has.<br />We have three zeros, so we are missing two!!!<br />By the Conjugate Pairs Theorem<br />Remaining zeros: -i, -2i<br />
9. 9.
10. 10. Example 3<br />Find a polynomial f of degree 4 whose coefficients are real numbers and that has the zeros 1, 1, 4+i. <br />
11. 11. By the Conjugate Pairs Theorem<br />
12. 12.
13. 13.
14. 14.
15. 15. Example 4: Use the given zero to find the remaining zeros of each function.<br />Note:<br />
16. 16. Zeros: 2i, -2i, 4<br />
17. 17. Example 5<br />
18. 18. Note: The resulting quadratic equation can not be factored since there is no number that multiplied gives you five and at the same time added gives you two.<br />
19. 19. We have to use completing the square or the quadratic formula<br />Quadratic Formula<br />Substitute <br />
20. 20. Simplify and solve!<br />Complex zeros:<br />Real zeros:<br />Remember the problem only asks for the complex zeros!<br />