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Methods for Advanced Mathematics (C3) Coursework Introduction: In this coursework, I am going to solve equations by using the Numerical Methods. The Numerical methods are used to solve equation that cannot be solved by using algebra. Here are the 3 Numerical methods: 1. Change of sign method 2. Newton-Raphson method 3. Rearranging f(x) = 0 in the form of x=g(x) Change of sign method This method is based on how an equation has a change of sign either from positive to negative or negative to positive on either side of a root when crossing the x-axis. It is best to sketch a diagram of the equation before starting with the method, so we would have a clear structure of what the equation looks like, the number of roots the equation has and the roots approximate position. To investigate this method I would use the following equation 0 = 3x3+11x2+2x-5 The graphs below show the function f(x) = 3x3+11x2+2x-5 x f(x) 6 1051 5 655 4 371 3 181 2 67 1 11 0 -5 -1 1 -2 11 -3 7 -4 -29 -5 -115 -6 -269 x (1dp) f(x) -1 1 -0.9 -0.077 As...

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