Everyday Usage and Use in Mathematics

In everyday language, zero refers to the number 0, which represents nothing or the absence of quantity; for example, "zero people" means no one is present. It's the point between positive and negative numbers on the number line.

Zeros of a function are the values where the function equals zero (\( f(x) = 0 \)), often where its graph crosses the x-axis. The term roots is sometimes used for the zeros of a polynomial.

Importance in Mathematics

Zeros of functions represent x-intercepts of the graph of a function. These points can provide significant information about the behavior of the function, such as changes in sign or the locations of critical points.

For example, finding the zeros of a quadratic function can help in determining the points where a projectile will land or the break-even points in a financial model. Zeros are also fundamental in calculus, particularly in the study of polynomial functions, as they help in solving equations and optimizing functions.