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Solving Equations Using Numerical Methods

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  • Essay length: 872 words
  • Submitted: 11/07/2012
  • Awarding body: AQA (for A-levels)
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AS and A Level Core & Pure Mathematics

The first 200 words of this essay...

Matt Coles Centre Number â 40120 Candidate Number - 3135

Solving Equations Using Numerical Methods

For my coursework, I am going to solve equations that cannot be solved analytically. This is when the equation would have been solved by using the quadratic formula, completing the square or by factorising it. The equations used will be solved numerically and there are three methods that I will be using:

1. The Change of Sign method

2. The Newton-Raphson method

3. The Rearrangement method

Method 1: The Change of Sign Method

The first method that I will be using is the Change of Sign method. The equation that I will be solving is y=x3+3x2-2x-1. To do this, I will be drawing the function of f(x)= x3+3x2-2x-1.

Root α

Root β

Root γ

To solve this equation using the Change of Sign method, I will be using the Decimal Search on Microsoft Excel.Firstly, I started by entering the equation into Autograph to get a sketch of the graph. This allowed me to work out that the three roots were between the integers of -4 and 1. These three roots are:

-4

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