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Quadratic Roots & The Carlyle Circle

Explore the Tschirnhaus transformation in quadratic equations and compare with cubic solutions, with practical applications and detailed examples. Discover the simplicity and efficiency of this method.

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Quadratic Roots & The Carlyle Circle

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  1. Quadratic Roots &The Carlyle Circle Ed Staples CMA 17 August 2019

  2. Tschirnhaus Transformation

  3. Quadratic formula

  4. The Tschirnhaus transformation

  5. The Tschirnhaus transformation

  6. Simple in application

  7. Simple in application

  8. Simple in application

  9. Simple in application

  10. Simple in application

  11. Simple in application

  12. Simple in application

  13. A Tschirnhaus transformation

  14. Task 1

  15. Task 1

  16. Task 1

  17. Task 1

  18. Task 1

  19. Task 1

  20. Task 1

  21. Task 1

  22. Compare with Cubic transformation

  23. Compare with Cubic transformation

  24. The cubic solution first steps

  25. The cubic solution first steps

  26. The cubic solution first steps

  27. Original cubic

  28. …divide by a

  29. Tschirnhaus transformationx=y+5

  30. Solutions by Descartes

  31. Descartes: 1st Type

  32. An example to follow

  33. Why it works…

  34. Check by completing squares

  35. Task 2

  36. Task 2

  37. Task 2

  38. Task 2

  39. Task 2

  40. Task 2

  41. Draw in the red oblique line

  42. Descartes: 2nd Type

  43. An example to follow

  44. Why it works…

  45. Check by completing squares

  46. Task 3

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