Maths change of sign coursework

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                Osaamah Mohammed

Maths A2 Coursework

Change of Sign Method:-

 

3x3 – 6x + 1 = 0

Sketch: -

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

Root [0 , 1]

X1 = 0

f(0) = 3(0)3 – 6(0) + 1 = 1

X2 = 0.1

f(0.1) = 3(0.1) 3 – 6(0.1) + 1 = 0.403

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Root [0.1 , 0.2]

Root [0.16 , 0.17]

Root [0.169 , 0.170]

Root [0.1690 , 0.1691]

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

Root = 0.169085 ± 0.000005

test        f (0.16908) = 0.00021

        f (0.16909) = -0.000036426

There is a change of sign, hence the root does lie in the interval [0.16908 , 0.16909]

Graphical Illustration


Rearrangement ...

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