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Pre-Calculus

Pre-Calculus. Unit 7: Lesson 2: Polynomial Equations. Warm-Up. Study your notes. There will be a 5 question timed quiz and an exit ticket at the end of the period today. Topic/Objective:. I will learn how to find all possible solutions, rational or irrational. Essential Question:.

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Pre-Calculus

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  1. Pre-Calculus Unit 7: Lesson 2: Polynomial Equations

  2. Warm-Up Study your notes. There will be a 5 question timed quiz and an exit ticket at the end of the period today.

  3. Topic/Objective: I will learn how to find all possible solutions, rational or irrational.

  4. Essential Question: How do find all zeros in a polynomial equation?

  5. Notes: Terminology Background: • Real Roots: • Physical x-intercepts • Factors that are real numbers • Numbers are rational • Complex Roots: • May not cross the x-axis • Might have imaginary numbers • Might have irrational or rational numbers

  6. Notes: Terminology Continued: • Rational Numbers: • Exact numbers • Irrational Numbers: • Non-exact and exact numbers • Could contain imaginary values

  7. Notes: Terminology Continued: • Double Roots: • A root that appears twice in a solution of an algebraic equation. • Depressed Polynomial: • A sad polynomial (just kidding) • Actually: New polynomial after dividing an original one by something.

  8. Finding Solutions: The Zero Product Rule: “If (A)(B)(C)=0, then either A = 0, B = 0, or C = 0” Example: (x + 8)(x – 1)(2x – 7) = 0 x + 8 = 0 x – 1 = 0 2x – 7 = 0 x = -8 x = 1 x = 7/2= 3.5

  9. Finding Irrational Solutions: You have done this in Algebra by using the…. Quadratic Formula: For the quadratic function ax2 + bx + c = 0 then:

  10. Your Assignment: Complete “Polynomial Equation” worksheets. If you do not finish them then it is homework. Quiz: Last ten minutes of class.

  11. Quiz Time!

  12. Exit Ticket: • Write at least three questions in the left hand column. • Summarize your notes by following the “Summary Paragraph Template” at your tables.

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