Roots of functions

Solving equations using roots of functions.

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Equivalence transformations Modify equations using equivalence transformations.
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Linear and quadratic equations Solving linear and quadratic equations.
Polynomial equations Solving polynomial equations of higher order.

Study Roots of functions

By subtracting one side, every equation in one unknown can equivalently be written in the form \(f(x)=0\).

Example 1. \[3x+4 = 5 \quad \Longleftrightarrow \quad 3x-1 = 0 \quad \Longleftrightarrow \quad f(x) = 0 \ \text{with $f(x) := 3x-1$.}\]

Important consequence:

The solutions of an equation are precisely the roots of the associated function.

One can often infer information of the solutions from the form of the associated function.

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