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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: -          ##### [-2,-1]  [0,1]  [1,2]

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

X1 = 0

Middle 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 0.00048043  0.170 -0.005261

#### Root [0.169 , 0.170]

 X f(X) 0.1690 0.00048043  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 0.00021  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

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) 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)

2

x = g(x)

Sketch : -

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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