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2. Wed 12/2 Lesson 5 – 5 Learning Objective: To apply Rational Root Thm (& Descartes’Rule) Hw: W.S. 5-5

3. Algebra II

4.  To understand & apply the Rational Root Theorem  To understand & apply the Conjugate Root Theorem  (To understand and apply Descartes’ Rule of Signs)

5. Look at COEFFICIENTS

6. q = 1 p = 12

7. q = 3 p = 10 Divide each numerator by each denominator

8. q = 1 p = 42

9. Step 2: Test each possible rational root in original function until you find a root.  Do synthetic substitution until get R0

10. 1 Nope! 1 is NOT a root! Try something else!

11. 2 YES! 2 IS a root!

12. q = 2 p = 6

13. YES! -1 IS a root!

18. 2 Sign Change 1 Sign Change + - 2 1 0 0 1 2  Sum = 3

19. 5 Sign Change 4 Sign Change

20. + - 5 4 0 5 2 2 5 0 4 3 4 2 3 2 4 3 0 6 1 4 4 1 2 6 1 0 8  It could have 5 positive roots, 4 negative roots, & 0 imaginary roots  It could have 3 positive roots, 2 negative roots, & 4 imaginary roots

21. 3 Sign Change 1 Sign Change + - 3 1 0 1 1 2 It could have 3 + roots, 1 - root, & 0 imaginary roots It could have 1 + roots, 1 - root, & 2 imaginary roots

22. q = 1 p = 6

23. 1 YES! 1 IS a root!