Algebra · Iteration
Chapter 1 · 3
The idea
Showing a root exists — change of sign
Why a sign change in a continuous function traps a root between two values, how to present the argument for full marks, and how the same idea justifies a root to a given accuracy.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Algebra · Iteration
Showing a root exists — change of sign
Why a sign change in a continuous function traps a root between two values, how to present the argument for full marks, and how the same idea justifies a root to a given accuracy.
Why it works
The equation you can't solve — but can trap
Try to solve . Nothing in the GCSE toolkit touches it — it doesn't factorise, and the quadratic formula is for quadratics. Yet the exam happily asks: "Show that the equation has a solution between and ." Two marks, no solving required — because proving a root exists somewhere is much easier than finding it. The trick is to trap it, and this equation will be our prey for the whole lesson.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
Start freeTakes a minute — no card.