Pure · Numerical methods
Chapter 1 · 4
The idea
Locating roots by change of sign
Trapping a root of f(x) = 0 in an interval using the change-of-sign rule — why continuity is essential, what a sign change does and doesn't guarantee, and refining a root to a given number of decimal places.
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Pure · Numerical methods
Locating roots by change of sign
Trapping a root of f(x) = 0 in an interval using the change-of-sign rule — why continuity is essential, what a sign change does and doesn't guarantee, and refining a root to a given number of decimal places.
Why it works
Trap it, then squeeze
Most equations cannot be solved exactly. There is no neat formula for the root of , and an equation like mixes a curve and a line in a way no rearrangement untangles. So instead of solving, you locate the root: first trap it in an interval, then squeeze that interval down.The change-of-sign rule
A root of is exactly where the graph crosses the -axis — where changes from negative to positive (or back). That is the whole idea:If is continuous on and and have opposite signs, then has a root somewhere between and .Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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