Zeros

Definition

Zeros of a function are the values of the variable that make the function equal to zero. For polynomial functions, they are also known as roots or solutions.

5 Must Know Facts For Your Next Test

1. Zeros can be real or complex numbers.
2. The number of zeros of a polynomial is equal to its degree, accounting for multiplicity.
3. Graphically, zeros correspond to the points where the graph intersects the x-axis.
4. In quadratic functions, zeros can be found using factoring, completing the square, or the quadratic formula.
5. For higher-degree polynomials, methods like synthetic division and the Rational Root Theorem are useful.

Review Questions

• What is the relationship between the degree of a polynomial and its number of zeros?
• How do you determine if a given value is a zero of a polynomial function?
• What methods can be used to find zeros in quadratic functions?

Related terms

Polynomial Function: A mathematical expression consisting of variables raised to non-negative integer powers and coefficients.

Quadratic Formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$, used to find the zeros of a quadratic equation $ax^2 + bx + c = 0$.

Multiplicity: The number of times a particular zero appears in a polynomial equation.