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Warm-Up 2/26

Warm-Up 2/26. 1. . J. Rigor: You will learn how to find the real and complex zeros of polynomial functions. Relevance: You will be able to use graphs and equations of polynomial functions to solve real world problems. . 2-4 Zeros of Polynomial Functions.

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Warm-Up 2/26

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  1. Warm-Up 2/26 1. J

  2. Rigor:You will learn how to find the real and complex zeros of polynomial functions.Relevance:You will be able to use graphs and equations of polynomial functions to solve real world problems.

  3. 2-4 Zeros of Polynomial Functions

  4. Example 1a: List possible rational zeros and determine which, if any are zeros. Step 1 Identify possible rational zeros. Step 2 Test possible rational zeros to determine if they are rational zeros. and There are no rational zeros.

  5. Example 1b: List possible rational zeros and determine which, if any, are zeros. Step 1 Identify possible rational zeros. Step 2 Test possible rational zeros to determine if they are rational zeros. – 1 4 0 – 12 – 9 1 – 3 3 – 3 – 9 1 9 – 1 – 3 3 ↓ – 3 0 9 ↓ – 9 1 3 – 3 0 1 0 – 3 0 There are two rational zeros at .

  6. Example 2: List possible rational zeros and determine which, if any, are zeros. Step 1 Identify possible rational zeros. Step 2 Test possible rational zeros to determine if they are rational zeros. – 2 8 – 7 – 22 3 4 – 13 4 3 – 6 26 – 8 ↓ – 4 12 ↓ 3 – 13 4 0 3 – 1 0 There are 3 rational zeros at .

  7. Example 6: Write a polynomial function of least degree with real coefficients in standard form that has the given zeros. 3 + i • (x – c) y = (x+ 2)(x – 4)[x – (3 – i)][x – (3 + i)] y = (x + 2)(x – 4)[(x – 3) + i][(x – 3) – i] y = (x² – 4x + 2x– 8)[(x – 3)² – i(x – 3) + i(x – 3) – i²] y = (x² – 2x– 8)[(x – 3)² + 1] y = (x² – 2x– 8)(x² – 6x + 9 + 1) y = (x² – 2x – 8)(x² – 6x + 10) y = x4 – 6x3 + 10x² – 2x3 + 12x² – 20x –8x² + 48x – 80 y = x4 – 8x3 + 14x² + 28x – 80

  8. Example 7: Write function as (a) the product of linear and irreducible quadratic factors and (b) the product of linear factors. Then (c) list all zeros. (a) the product of linear and irreducible quadratic factors

  9. Example 7: Write function as (a) the product of linear and irreducible quadratic factors and (b) the product of linear factors. Then (c) list all zeros. (b) the product of linear factors (c) List all zeros There are 5 zeros: .

  10. Example 8: Use given zeros to find all complex zeros. Then write the linear factorization of the function. 2 – 3i – 6 20 – 13 1 – 22 2 – 3i 24 + 3i – 17 + 6i ↓ 13 – 4 – 3i 1 3 + 6i 2 + 3i 0 2 + 3i 1 – 4 – 3i 3 + 6i 2 + 3i – 2 – 3i 2 + 3i – 4 – 6i ↓ 1 – 2 – 1 0

  11. Example 8: Use given zeros to find all complex zeros. Then write the linear factorization of the function.

  12. math! • 2-4 Assignment: TX p127, 4-16 EOE & 32-52 EOE

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