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Term 2 grade 11 core project Due date :4 march 2012 The polynomial project Preparing:

Term 2 grade 11 core project Due date :4 march 2012 The polynomial project Preparing: Omran Mohammed Ali AT1001693@IAT.AC.AE Suhail Salem Alafari AT1000110@IAT.AC.AE Mohammad adulrahman salman. Task ( 1 ). A-Find the polynomial that gives the following values.

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Term 2 grade 11 core project Due date :4 march 2012 The polynomial project Preparing:

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  1. Term 2 grade 11 core project Due date :4 march 2012 • The polynomial project • Preparing: • Omran Mohammed Ali AT1001693@IAT.AC.AE • Suhail Salem Alafari AT1000110@IAT.AC.AE • Mohammad adulrahman salman

  2. Task ( 1 )

  3. A-Find the polynomial that gives the following values

  4. Write the system of equations in A, B, C, andD that you can use to find the desired polynomial. • A=10 • -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)+D (5-(-1)) (5-1)(5-2)

  5. B- Solve the system obtained from part a. • A=10 • -6=A+2B B = -8 • -17=A+3B +3C C = -1 • 82= A+ 6B + 24C + 72 D D= 2

  6. C- Find the polynomial that represents the four ordered pairs • -17=10+3(-8)+3c • -17-10+24=3c • -3=3c • 82=10+6(-8)+24(-1)+72d • 82-10+48+24=72d • 144=72d • A=10 B=-8 C=-1 D=2

  7. 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)

  8. The bisection method can be used to approximate zeros of polynomial functions like fx=x3+x2-3x-3 • P(x)=2x³-5x²-10x+7

  9. Task ( 2 )

  10. Find the zeros of the polynomial found in task 1 • PC(-1)=2(-1)³-5(-1)²-10(-1)+7=10 • P(-2)=2(-2)³-5(-2)²-10(-2)+7=-9 • P(0) • P(1) • P(3)=-14 • P(4)=15

  11. Find to the nearest tenth the third zero using the Bisection Method for Approximating Real Zeros. • P(3.5)=-3.5 • Midpoint=3-5+4/2. P(3.75)=4.65625 • Midpoint=3.625+3.5/2= P(3.625)= 0.3164 • Midpoint=3>625+3.5?2= P(3.5625)=-1.6557 • The zero is 3.6 to the nearest tenth

  12. Task ( 3 )

  13. Choose any value for the width of the walkway w that is less than 6 ft • W=5ft

  14. Write an expression for the area of the garden and walk. • Area=LxW • =(2x+10)(x+10) • 2x²+20x+10x+100 • Area=2x²+30x+100 • Width x+5+5 • Length 2x+5+5 • Area of garden =2x²x(2x)

  15. Write an expression for the area of the walkway only • =30x+100 • Area(garden+walk)-Area(garden) • 2x²+30x+100-(2x²)

  16. 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=1000-100 • 30x/30=900/30 • X=30ft • The dimension of garden • Width x=30 ft • Length 2x+2(30)=60ft

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