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The Polynomial Project

The Polynomial Project. Don By : Ateeq Eid AlDhaheri & Ahmed Alzarouni Section : 11.02. Introduction :

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The Polynomial Project

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  1. The Polynomial Project Don By : AteeqEidAlDhaheri & Ahmed Alzarouni Section : 11.02

  2. Introduction: The concept of degree of a polynomial is important, because it give us information about the behavior of the polynomial on the whole. The concept of polynomial functions goes way back to Babylonian times, as a simple need of computing the area of a square is a polynomial, and is needed in buildings and surveys, fundamental to core civilization. Polynomials are used for fields relating to architecture, agriculture, engineering fields such as electrical and civil engineering, physics, and various other science related subjects.

  3. Task 1: Find the polynomial that gives the following values x -1 1 2 5 p(x) 10 -6 -17 82

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

  5. The diagram below summarizes the results obtained by the bisection method.

  6. Task 2: Find the zeros of the polynomial found in task 1. • Show that the 3 zeros of the polynomial found in task 1 are: • First zero lies between -2 and -1 • Second zero lies between 0 and 1 • Third zero lies between 3 and 4.

  7. 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.

  8. Task 3: 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.

  9. 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. rea=2x+10x+10 =2x2+20x+10x+100 =2x2+30x+36 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

  10. You have enough gravel to cover 1000ft2 and want to use it all on the walk. How big should you make the garden? • 30x+100=1000 • 30x=1000-100 • 30x=900 • x=30 • 2(30)2=1800ft2

  11. Task 4: Using Technology: • Use a graphing program to graph the polynomial found in task 1

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