Mathematics (AS)·Numerical solutions of equations · NSSCAS 2.6.1
Locating roots of equations
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Some equations simply cannot be solved with algebra, so instead we hunt down their roots approximately. In this lesson you will find a root two ways: roughly by sketching two graphs and reading where they cross, then tightly by searching for a change of sign. You will also meet a sequence of approximations that marches ever closer to the true root, and learn to write it as xₙ → α. Calm, careful and step by step, the way Miss Eve teaches.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 2.6.1):
- Locate a root of an equation approximately using graphical considerations — rearranging into f(x) = g(x) and reading off where the two curves intersect.
- Locate a root by searching for a sign change: if f(a) and f(b) have opposite signs and f is continuous, a root lies between a and b — and narrow the interval further.
- Interpret a sequence of approximations x₁, x₂, x₃, … that converges to a root of an equation, and use the notation xₙ → α.
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