The root of
an equation is any number which satisfies the equation. It is a
solution of the equation.
x = 2 is a root of 3x - 1 =
5, as 3 x 2 - 1 = 5, and of x2 - 3x + 2 = 0, as 22 - 3
x 2 + 2 = 0.
But x = 1 is also a root of the second equation as 12
- 3 x 1 + 2 = 0.
Equations are often used to state the equality of two expressions
containing one or more variables. In the reals we can say, for example,
that for any given value of x it is true that
x(x - 1) = x2 - x.
(x + 1)2 = 2x2 + x + 1 is an equation, whose roots are x = 0 and
x = 1. Whether a statement is meant to be an identity or an equation,
carrying information about its variables can usually be determined
from its context.