Root of an equation

A root of an equation is a value of its unknown that makes the equation true. For an equation $f(x)=0$, it is a zero of a function. More generally, roots of $f(x)=g(x)$ are zeros of $f-g$, provided both sides are defined at the candidate value.

For example, $x^2=4$ has the real roots $2,-2$. Clearing a denominator requires checking the original domain: solving $(x^2-1)/(x-1)=0$ permits $x=-1$ but not $x=1$. The coefficient field also matters, since $x^2+1=0$ has no real root but has two complex roots.