Algebra 70 - The Zero Product Property

The "zeros" or "roots" of a quadratic function of a real variable x, correspond to the function's x-intercepts. It is not always easy to find the zeros of a quadratic function. However, quadratic functions can be factored into the product of two linear functions. The "zero product property" then tells us that every zero of a quadratic function will occur as a zero of at least one of the linear functions that are its factors. Therefore, if we can factor the quadratic, we can find its zeros by finding the zeros of its linear factors, which is typically much easier.