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The Polynomial Project

The Polynomial Project. Prepared by : Mohammed Rashed AlBaik, Younes Ali AlMahrouqi and Abdulla Mohammed Albaloushi. Class : 11.04. Task 1 : Find the polynomial that gives the following values. Write the system of equations in A, B, C, and D that you can use to find the desired polynomial.

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The Polynomial Project

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  1. The Polynomial Project Prepared by: Mohammed Rashed AlBaik, Younes Ali AlMahrouqi and Abdulla Mohammed Albaloushi • Class: 11.04

  2. Task 1: Find the polynomial that gives the following values

  3. Write the system of equations in A, B, C, and D that you can use to find the desired polynomial

  4. Solve the system obtained from part a.

  5. Solve the system obtained from part a.

  6. Find the polynomial that represents the four ordered pairs.

  7. Write the general form of the polynomial of degree 4 for 5 pairs of numbers.

  8. The Bisection Method for Approximating Real Zeros • Find the zeros of the polynomial found in task 1.

  9. Find to the nearest tenth the third zero using the Bisection Method for Approximating Real Zeros. Since f (3) = -14 and f (4) = 15, there is at least one real zero between 3 and 4. The midpoint of this interval is 3.5. Since f (3.5) = -3.5, the zero is between 3.5 and 4. The midpoint of this interval is 3.7. Since f (3.7) is about 2.856, the zero is between 3.5 and 3.7. The midpoint of this interval is 3.6. Since f (3.6) is about -0.488. The zero is between 3.6 and 3.7. The midpoint of this interval is 3.65. Since f (3.65) is about 1.14, the zero is between 3.6 and 3.65. The midpoint of this interval is 3.625. Since f (3.61) is about -0.168, the zero is between 3.6 and 3.625. Therefore, the zero is 3.6 to the nearest tenth.

  10. Real World Construction You are planning a rectangular garden. Its length is twice its width. You want a walkway w feet wide around the garden. Let x be the width of the garden.

  11. a. Choose any value for the width of the walkway w that is less than 6 ft. W = 5 length= 10 • Write an expression for the area of the garden and walk. • Area=2x+10x+10 • =2x2+20x+10x+100 • =2x2+30x+36

  12. c. Write an expression for the area of the walkway only. • 2(2x+105)+2(5x) 2((10x + 50)) + 10 x 20x+100+10x 30x+100

  13. Using Technology:Use a graphing program to graph the polynomial found in task 1

  14. The End Wiki : http://think4math.wikispaces.com/file/detail/Math+project+.pptx

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