Real Equation Solutions
Why
Given a real valued function (e.g., a polynomial) how do we compute its roots?
Definition
Given $f: \R \to \R $, we call $f(x) = 0$ a nonlinear equation (a nonlinear homogenous equation). If $x \in \R $ with $f(x) = 0$ we call $x$ a root or solution of $f$.
Examples
For a classic example, suppose $s \in \R $ is
given and consider the function $f: \R \to
\R $ defined by
\[
f(t) = t - \sqrt{s}
\] \[
0 = r - \sqrt{s} \Rightarrow r = \sqrt{s}
\]