Zeros of a function

Definition

Zeros of a function are the points where the function's value is equal to zero. These are the \(x\)-values for which \(f(x) = 0\).

5 Must Know Facts For Your Next Test

1. Zeros of a function are also called roots or solutions.
2. The zeros can be found by solving the equation \(f(x) = 0\).
3. A polynomial of degree \(n\) can have at most \(n\) real zeros.
4. If a function crosses the x-axis, those points are its zeros.
5. The multiplicity of a zero indicates how many times that zero occurs as a root.

Review Questions

• What is another name for the zeros of a function?
• How do you find the zeros of a given function?
• What does it mean if a zero has multiplicity greater than one?

Related terms

Roots: The values of \(x\) that satisfy the equation \(f(x) = 0\), synonymous with zeros.

Polynomial: A mathematical expression consisting of variables, coefficients, and exponents combined using addition, subtraction, multiplication, and non-negative integer exponents.

Multiplicity: The number of times a particular root is repeated for a polynomial equation.