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    Maths change of sign coursework

    Extracts from this document...

    Introduction

                    Osaamah Mohammed

    Maths A2 Coursework

    Change of Sign Method:-

    3x3 – 6x + 1 = 0

    Sketch: -

    image15.pngimage25.pngimage33.pngimage31.pngimage25.pngimage25.pngimage09.pngimage14.pngimage00.pngimage01.png

    Looking at the graph we find that the roots lie between these intervals:
    [-2,-1]  [0,1]  [1,2]

    Finding root interval between [0,1] using a Decimal Search

    image03.pngimage32.pngimage04.pngimage02.pngimage34.pngimage06.pngimage05.pngimage06.png

    Root [0 , 1]

    X1 = 0

    ∴

    ...read more.

    Middle

    image07.png

    0.17

    -0.005261

    Root [0.16 , 0.17]

    X

    f(X)

    0.16

    0.052298

    0.161

    0.046520

    0.162

    0.040755

    0.163

    0.034992

    0.164

    0.029233

    0.165

    0.023476

    0.166

    0.017723

    0.167

    0.011972

    0.168

    0.0062249

    0.169

    0.00048043image08.pngimage07.png

    0.170

    -0.005261

    Root [0.169 , 0.170]

    X

    f(X)

    0.1690

    0.00048043image07.pngimage08.png

    0.1691

    -0.0000923852

    Root [0.1690 , 0.1691]

    X

    f(X)

    0.1690

    0.00048043

    0.16901

    0.00042299

    0.16902

    0.00036557

    0.16903

    0.00030814

    0.16904

    0.00025071

    0.16905

    0.00019328

    0.16906

    0.00013586

    0.16907

    0.00078427

    0.16908

    0.00021image08.pngimage07.png

    0.16909

    -0.000036426

    From this method we find that the root lies between[0.16908 , 0.16909]

    ∴ Root = 0.169085 ± 0.000005

    testf (0.16908) = 0.00021

            f (0.16909) = -0.000036426

    There is a change

    ...read more.

    Conclusion

    Start X1 = 0        Use Xn+1 = 2xn3 + 1
                                               5

    X2 = 2(0)3 + 1 = 0.2      

                      5

    X3 = 2(0.2)3 + 1 = 0.216      

                      5

    X4 = 2(0.216)3 + 1 = 0.22016      

                      5

    X5 = 0.22134

    X6= 0.22169

    X7 = 0.22179

    X8 = 0.22182

    X9 = 0.22183                        root to 5 s.f (took 9 iterations)image30.png

    X10 = 0.22183

    Failure: -

    Solve 2x3 – 5x + 1 = 0

    Re-arrange this so that “X=….”

    • 2x3 – 5x + 1 = 0

          2x3 +1 = 5x

          2x3 = 5x – 1

          x3 = 5x – 1

                     2

          x = (5x – 1)⅓

                     2

          x = g(x)

    Sketch : -

    ...read more.

    This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics section.

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