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Term 2 Grade 11 Core Project The Polynomial Project

Term 2 Grade 11 Core Project The Polynomial Project. Student Name: Mansour Obaid AlMashaikhi Student Name: Saif Jamal AlKaabi Grade: 11.04. Introduction:.

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Term 2 Grade 11 Core Project The Polynomial Project

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  1. Term 2 Grade 11 Core ProjectThe Polynomial Project Student Name: Mansour ObaidAlMashaikhi Student Name: Saif Jamal AlKaabi Grade: 11.04

  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 p(x)= A+B(x-x0)+C(x-x0)(x-x1)+D(x-x0)(x-x1) (x-x2)

  4. a. Write the system of equation in A, B, and D that you can use to find the desired polynomial. • 10= A • -6= A+B(1- -1) • -17= A+B(2- -1)+C(2- -1)(2- 1) • 82= A+B(5- -1) +C(5- -1) (5- 1)(5-2) b. Solve the system obtained from part a. A=10 B= -8 C= -1 D= 2

  5. C. Find the polynomial that represents the four ordered pairs. • p(x)= A+B(x-x0)+C(x-x0)(x-x1)+D(x-x0)(x-x1) (x-x2) Simplify:p(x)= 10+-8(x- -1)+-1(x- -1)(x-1)+2(x- -1)(x-1) (x-2) P(x)= 2x3-5x2-10x+7 D. Write the general form of the polynomial of degree 4 for 5 pairs of numbers. • p(x)= A+B(x-x0)+C(x-x0)(x-x1)+D(x-x0)(x-x1) (x-x2)+E(x-x0)(x-x1) (x-x2)(x-x3)

  6. Task 2: Find the zeros of the polynomial found in task 1. • a. Show 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. b. Find 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 interval is 3.5 . • Since F(3.5)= -3.5, the zero is between 3.5 and 4. • The midpoint of this interval is 3.75 . • Since f(3.75) is about 4.66 . • Therefor, 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. a. Choose any value for the width of the walkway w that is less than 6 ft. • w= 4 ft b. Write an expression for the area of the garden and walk. Area= (2x+8) (x+8) =2x2+16x+8x+64 =2x2+24x+64

  10. c. Write an expression for the area of the walkway only. Area= 8(2x+8)+8x = 16x+16+8x =24x+16 D. You have enough gravel to cover 1000ft2 and want to use it all on the walk. How big should you make the garden? 1000= 24x+16 1000-16= 24x 984/24= 24x/24 x= 41 Area of garden= 2x2 = 2(41)2 = 3362 ft2

  11. Wiki link: http://mansouralmashaikhi.wikispaces.com/

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