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5-Minute Check Lesson 4-4A

5-Minute Check Lesson 4-4A. Math ador Gameplan. Section 4.4: The Rational Root Theorem CA Standards: MA 4.0 Daily Objective (10/15/12):

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5-Minute Check Lesson 4-4A

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  1. 5-Minute Check Lesson 4-4A

  2. MathadorGameplan Section 4.4:The Rational Root Theorem CA Standards:MA 4.0 Daily Objective (10/15/12): Students will be able to (1) identify all possible rational roots of a polynomial equation by using the Rational Root Theorem, and (2) determine the number of positive and negative real roots a polynomial function has. Homework: page 234 (#10 to 23 all, 26)

  3. Use the remainder theorem to evaluate each function g(x) = x4 + x2 + 2, g(3) q(x) = x5 + 32, q(-2) Determine the binomial factors of the given polynomials. x3- 6x2 + 11x – 6

  4. Information about the Rational Root Theorem • Provides a list of possible rational roots of a polynomial function • Not every number will be a root • Does not provide a complete list

  5. List all possible roots of f(x) = -x4 + 3x2 + 4

  6. Use the Rational Roots Theorem and trial & error to find a rational root • Once the polynomial is reduced to a quadratic then use factoring or the quadratic formula to find the remaining roots.

  7. List all possible roots of 6x3 + 11x2 – 3x – 2 = 0 Then determine the rational roots.

  8. Find the roots of x3 + 8x2 + 16x + 5 = 0

  9. List all possible rational zeros • f(x) = 4x5 + 12x4 – x – 3 • Find all zeros • f(x) = x3 + 8x2 + 11x – 20 • f(x) = x3 + x2 – 5x – 2 • Solve • x4 – 6x3 + 22x2 – 30x + 13 = 0

  10. Descartes’s Rule of Signs 1. The number of positive real zeros of f is either • The same as the number of sign changes of f(x) OR • Less than the number of sign changes by an even integer Note: if f(x) has only one sign change, then f has only one positive real zero 2. The number of negative real zeros of f is either • The same as the number of sign changes of f(-x) OR • Less than the number of sign changes by an even integer Note: if f(-x) has only one sign change, then f has only one negative real zero

  11. Find the number of possible positive real zeros and the number of possible negative real zeros for f(x) = x4 – 5x2 + 4

  12. Find the number of possible positive real zeros and the number of possible negative real zeros for f(x) = 2x5 + 3x4 – 6x3 + 6x2 – 8x + 3

  13. Determine the possible numbers of positive and negative real zeros of f(x) = x3 + 2x2 + 5x + 4

  14. Determine the possible numbers of positive and negative real zeros of f(x) = x4 - 14x3 + 71x2 – 154x + 120

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