Numerical solutions of equations

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A2 Mathematics Coursework C3

Year 12

Numerical solutions of equations

Solving 0 = x5+x-5 using the "Change Of Sign" Method

The method I will use to solve 0 = x5+x-5 is the Change of Sign Method involving the Decimal Search method. I have drawn this graph using the Autograph Software, and the print screen of this is below:

From my graph above, I can see that the root of this equation is between x =1 and x = 1.5. The table of x values and f(x) values is shown below. I can work out the f(x) values by substituting the x-values into the equation.

x

1

1.1

1.2

1.3

1.4

1.5

f(x)

-3

-2.28949

-1.31168

0.01293

1.77824

4.09375

From my table of values above, it is clear that the change of sign from negative to positive occurs between x = 1.2 and x = 1.3. So, I can narrow these values down further to find another change of sign.

x

f(x)

1.21

-1.19626

1.22

-1.07729

1.23

-0.95469

1.24

-0.82837