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Warm Up. Find all zeros. Graph.

Learn how to find & graph all zeros of an nth-degree polynomial, incorporating the Rational Root & Fundamental Theorem of Algebra. Understand the concept of complex zeros, their multiplicity, and the significance of synthetic division & the Quadratic Formula in finding solutions. Practice writing polynomials with given zeros & solving for roots in complex number systems.

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Warm Up. Find all zeros. Graph.

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  1. Warm Up. Find all zeros. Graph.

  2. Warm Up. Find all zeros. Graph. Touches Through

  3. More on Rational Root Theorem

  4. Fundamental Theorem of Algebra • In the complex number system, an nth degree polynomial has precisely “n” zeros.

  5. Find all zeros. Goes through both!

  6. Find all zeros.

  7. Find all zeros. Multiplicity of 2. Just Touches.

  8. Find all zeros.

  9. Find all zeros.

  10. Find all zeros.

  11. Find all zeros.

  12. Find all zeros.

  13. Find all zeros.

  14. Find all zeros.

  15. Find all zeros. Using the remainder theorem we see that there are NO real solutions!

  16. Find all zeros.

  17. Find all zeros. Synthetic division gets you to the following: Now use the Quadratic Formula for this part.

  18. Find all zeros.

  19. Find all zeros. Synthetic Division gives Multiplicity of 2

  20. Find all zeros.

  21. Find all zeros. Synthetic Division gives Quadratic Formula completes it.

  22. Complex Conjugates

  23. Always come in conjugate pairs Complex Zeros

  24. Write a polynomial with the given zeros: 2, i, -i

  25. Write a polynomial with the given zeros: 3, 4i Remember – they come in pairs!

  26. Write a polynomial with the given zeros: 4, 2-3i

  27. Find all zeros, given that (2i) is a root.

  28. Find all zeros, given that (3 – 5i) is a solution.

  29. Find all zeros, given that (3 – 5i) is a solution.

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