Number Iterations
Maths: Edexcel A Level Pure Maths, topic 9.1.1
Approximate Solutions
Find the approximate solution to x³ - 3x + 1 = 0:
Write the equation
Sub in a trial solution x = 1
- This is just an educated guess, we could use any number but we think
x = 1 will be roughly right.
This gives -1
-1 is less than 0 so is below our target
Sub in our second guess, x = 2
This gives 3
3 is more than 0 so is above our target
Approximation of x
- x = 1 gives a result below 0
- x = 2 gives a result above 0
- Therefore the x value which gives exactly 0 must be in between 1 and 2.
Function notation
- f(x) = x3 - 3x + 1 so we can write the solution like this.