Interval Bisection (Edexcel International AS Further Maths)

Interval Bisection

What is interval bisection?

• Interval Bisection means splitting an interval containing a root into two halves and using a sign change test to find out which half contains the root

• For example, if and and is continuous

  • Then a root must lie in

  • Find the midpoint of the interval

    • 

  • Check the sign at the midpoint

    • For example,

  • Write down the half-interval that has the sign change

    • , and

    • So has the sign change

• The process can be repeated

  • For example, if then contains the sign change

How do I use interval bisection to estimate a root?

• If a root lies in the interval , then the first approximation of the root, , is simply the midpoint

  • 

• The second approximation, , requires using Interval Bisection once

  • For example, giving

  • Then find the midpoint

    • 

  • And so on