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In this piece of coursework, I will use three different methods (Change of Sign, Newton-Raphson, and the Rearrangement Method) to find the roots of a series of different equations. The number of roots found differs from method to method.  

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Pure Mathematics 2: Coursework Assessment In this piece of coursework, I will use three different methods (Change of Sign, Newton-Raphson, and the Rearrangement Method) to find the roots of a series of different equations. The number of roots found differs from method to method. A comparison of the three methods will be made at the end of the report. Change of Sign Method Equation: x3 + x2 - 2x + 3 = 0 Using the above equation, the function f(x) = x3 + x2 - 2x + 3 may be generated. This may be expressed in graphical form (see page 2) This may be solved using the method of Interval Bisection (see page 3) <--------Interval-------> Mid Point Height at A Height at B Height at M Curve a b Mid Point f(a) f(b) f(m) y=x^3+x^2-2*x+3 -3 -2 -2.5 -9 3 -1.375 -2.5 -2 -2.25 -1.375 3 1.171875 -2.5 -2.25 -2.375 -1.375 1.171875 -0.005859375 -2.375 -2.25 -2.3125 -0.005859375 1.171875 0.606201172 -2.375 -2.3125 -2.34375 -0.005859375 0.606201172 0.306060791 -2.375 -2.34375 -2.359375 -0.005859375 0.306060791 0.151584625 -2.375 -2.359375 -2.3671875 -0.005859375 0.151584625 0.073235035 -2.375 -2.3671875 -2.37109375 -0.005859375 0.073235035 0.033781111 -2.375 -2.37109375 -2.373046875 -0.005859375 0.033781111 0.013984211 -2.375 -2.373046875 -2.374023438 -0.005859375 0.013984211 0.004068256 -2.375 -2.374023438 -2.374511719 -0.005859375 0.004068256 -8.94099E-04 -2.374511719 -2.374023438 -2.374267578 -8.94099E-04 0.004068256 0.001587443 -2.374511719 -2.374267578 -2.374389648 -8.94099E-04 0.001587443 3.46763E-04 The root 'x' can be seen to be in between -2.374511719 and -2.374267578 ie. -2.374511719

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