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Warm – up #5

Learn how to write polynomial functions with rational coefficients using given roots. Practice assignments included.

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Warm – up #5

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  1. Warm – up #5 1. and are roots of P(x), find two other roots and 2. and are roots of P(x), find one other root.

  2. Homework Log

  3. 12/3/15 Lesson 5 – 5 Writing Equations Given Roots Day 2 Algebra II

  4. Learning Objective • To write polynomial equations given its roots • To remember how to find rational roots

  5. Write a Polynomial Function From its Roots 1. Write a polynomial function with rational coefficients so that P(x) = 0 has the given roots of 7 and –2 x = –2 x = 7 x + 2 = 0 x – 7 = 0 (x + 2)(x – 7) = 0

  6. Write a Polynomial Function From its Roots 2. Write a polynomial function with rational coefficients so that P(x) = 0 has the given roots of and  must also be a root! x = x = x = 2x =1 x – = 0 x + = 0 (2x – 1)(x - )(x + ) = 0

  7. (2x – 1)(x - )(x + ) = 0 - x –1 2x x –x – -9 x -9 = 9 9 18x -9

  8. Write a Polynomial Function From its Roots 3. Write a polynomial function with rational coefficients so that P(x) = 0 has the given roots of and  must also be a root! x = x = x = x + 3 = 0 x=0 x=0 (x + 3)(x)(x) = 0

  9. (x + 3)(x)(x) = 0 (x + 3) = 0 -2 x -2x -2 -2x 4 = 25

  10. (x + 3)= 0 x 29x -4 29 –4x 3 87 3 -12x

  11. Write a Polynomial Function From its Roots 4. Write a polynomial function with rational coefficients so that P(x) = 0 has the given roots of and  must also be roots! x= x= x= x= = 0

  12. = 0 3 -7 3x x x -7x x 3 9 3x -7 49 -7x x x = -2 = 9

  13. 7 6 7 6 -14x -14 –84 -98x 58 406 58 348x

  14. Write a Polynomial Function From its Roots 5. Write a polynomial function with rational coefficients so that P(x) = 0 has the given roots of and  must also be a root! x = x = x = x – 1 = 0 x=0 x=0 (x – 1)(x)(x) = 0

  15. (x – 1)(x)(x) = 0 - x –1 x x –x – x = -20 -20 20 -20x

  16. Write a Polynomial Function From its Roots 6. Write a polynomial function with rational coefficients so that P(x) = 0 has the given roots of and  must also be a root! x = x = x = 3x = -4 x – 2 = x – 2 = 3x+4 = 0 x=0 x=0 (3x+4)(x(x)=0

  17. (3x+4)(x(x)=0 (3x + 4) = 0 -2 x -2x -2 -2x 4 = -63

  18. (3x + 4) = 0 3x -177x -12 -59 –4x 4 -236 4 -16x

  19. Applying Rational Root Theorem 7. What are the rational roots of q = 6 p = 15 = = , , , , , , , , , ,

  20. Applying Rational Root Theorem 7. Nope! 1 is NOT a root! 1 - Yes! -IS a root! Use these #s for the next synthetic check!

  21. Applying Rational Root Theorem 7. YES! IS a root! Solve =0 =0 NO MORE RATIONAL ROOTS! x = Rational Roots: and

  22. Descartes’ Rule of Signs 8. 3 Sign Change 1 Sign Change + - It could have 3 + roots, 1 - root, & 0 imaginary roots 0 3 1 2 1 1 It could have 1 + roots, 1 - root, & 2 imaginary roots

  23. Ticket Out the Door • Write a polynomial function with rational coefficients so that P(x) = 0 has the roots –1, , and

  24. Assignment:Pg. 315#23 – 29 odd, 37 – 41 odd, 42, 45

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