root

A root of a function is an input that makes its output exactly zero. If you think of the function as a machine, the roots are the special settings where the machine produces nothing — output 0. They are also called the zeros of the function.

For an equation like ax^2 + bx + c = 0, a root means the same thing: a value of x that makes the statement true, that is, a solution. Graphically, the real roots are precisely where the curve crosses or touches the x-axis — the x-intercepts. A quadratic can have two, one, or zero real roots.

“Root” has a second, related meaning to keep distinct: in “square root” or “cube root” it refers to the inverse of raising to a power. Both senses share the historical image of a quantity that, planted in the equation, makes it grow to zero. Context tells you which is meant.