Table of Contents

## What are distinct zeros on a graph?

Distinct zeros mean different values of x. Getting to the Answer: You are looking for the graph that has four different x-intercepts, or in other words, crosses through the x-axis four times, which is the graph in (D). Note that the graphs in A and C have two distinct zeros, and the graph in B has three.

**What does distinct real number zeros mean?**

A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.

### How many distinct zeros does a polynomial have?

The polynomial p(x)=(x-1)(x-3)² is a 3rd degree polynomial, but it has only 2 distinct zeros. This is because the zero x=3, which is related to the factor (x-3)², repeats twice. This is called multiplicity. It means that x=3 is a zero of multiplicity 2, and x=1 is a zero of multiplicity 1.

**What is the purpose of finding zeros?**

As we learned, finding the zero of a function means to find the point (a, 0) where the graph of the function and the y-intercept intersect. To find the value of a from the point (a, 0), you need to set the function equal to zero and then solve for x.

#### Are multiplicities real zeros?

The real (that is, the non-complex) zeroes of a polynomial correspond to the x-intercepts of the graph of that polynomial. A zero has a “multiplicity”, which refers to the number of times that its associated factor appears in the polynomial.

**Can a function have no zeros?**

Each value a1,a2 a 1 , a 2 , and so on is a zero. A polynomial function may have many, one, or no zeros. For example, a cubic function can have as many as three zeros, but no more. This is known as the fundamental theorem of algebra.

## What is a function with no zeros?

The sine function has no algebraic zeros except 0, but has infinitely many transcendental zeros: −3π, −2π, −π, π, 2π, 3π,. . . The multiplicity of a zero of a polynomial is how often it occurs.

**What does number of zeros mean?**

The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

### What are multiplicities of zeros?

**How do you find the zeros of each function?**

To find a zero of a function, perform the following steps: Graph the function in a viewing window that contains the zeros of the function. Set the Format menu to ExprOn and CoordOn. Press [2nd][TRACE] to access the Calculate menu. Press [2] to select the zero option. If necessary, repeatedly press Set the Left Bound for the zero you desire to find.

#### What are the possible rational zeros of?

Place the polynomial in descending order.

**Which real numbers are zeros of the function?**

A real zero of a function is a real number that makes the value of the function equal to zero. A real number, r , is a zero of a function f , if f ( r ) = 0 . Example: Find x such that f ( x ) = 0 . Since f ( 2 ) = 0 and f ( 1 ) = 0 , both 2 and 1 are real zeros of the function.

## What are complex zeros?

A complex zero is a complex number (one with both a real part and an imaginary part) that when plugged into the function causes the function to evaluate to zero. Some functions do not have any zeros that can be expressed using only real numbers, but do have one or more zeros that can be expressed using complex numbers.