The online **Multiplicity Calculator** allows you to find the **zeros** of an equation.

The online **Multiplicity Calculator** is a powerful tool used by mathematicians and physicists to find the zeros or roots of an equation. The **Multiplicity Calculator** plays a vital role in solving complex mathematical problems.

## What Is a Multiplicity Calculator?

**A Multiplicity Calculator is an online calculator that allows you to find the zeros or roots of a polynomial equation you provide.**

The **Multiplicity Calculator** requires a single input, an equation you provide to the **Multiplicity Calculator**. The equation must be a polynomial function for the **Multiplicity Calculator** to work. The **Multiplicity Calculator** calculates the results instantly and displays them in a new window.

The **Multiplicity Calculator** displays several results such as the **roots** of the equation, **root plot** of the equation, **number line** of the equation, the sum of roots, and the product of roots.

## How To Use a Multiplicity Calculator?

You can use the **Multiplicity Calculator** by entering your **polynomial equation** and clicking the “Submit” button. The results would be instantly displayed on your screen.

The step-by-step instructions on how to use a **Multiplicity Calculator **are given below:

### Step 1

In the first step, you plug your polynomial equation into the **input box** provided in your **Multiplicity Calculator**.

### Step 2

After entering your polynomial equation in the** Multiplicity Calculator,** you click the **“Submit” **button. The calculator will display the results in a separate window.

## How Does a Multiplicity Calculator Work?

A **Multiplicity Calculator** works by calculating the **zeros** or the **roots** of a polynomial equation. A polynomial equation $ax^{2} + bx + c $ usually intercepts or touches the x axis of a graph; the equations are solved and are put equal to zero to calculate the **roots** of the equation.

Let’s discuss some important concepts related to the working of this calculator.

## What Are Zeros of Polynomials?

**Zeros**** of polynomials** are points where the polynomial equations become equal to zero. In layman’s terms, we can state that a polynomial’s zeros are variable values at which the polynomial equals 0.

The zeros of a polynomial are often referred to as the equation’s **roots** and are frequently written as $\alpha$,$\beta$, and $\gamma$.

In mathematical terminology, the values of x that fulfill the polynomial f(x) = 0 equation are the **zeros**** of polynomial**. In this case, the polynomial’s **zeros** are the x values for which the function’s value, f(x), equals zero. The degree of equation f(x) = 0 determines how many zeros a polynomial has.

## How To Find Zeros of Polynomials?

You can find **zeros** of the polynomial by substituting them equal to 0 and solving for the values of the variable involved that are the zeros of the polynomial.

Finding a polynomial’s **zeros** can be done in a variety of ways. The degree of the polynomial equation determines how many **zeros** the polynomial has.

To determine the zeros of the polynomial, each of the numerous equations—which have been categorized as **linear, quadratic, cubic**, and **higher degree polynomials**—is individually examined.

The different polynomial equations with the methods to solve them are given below:

### Finding Zeros for Linear Equations

**Linear equations** are generally written as y = ax + b. You may find the solution to this equation by substituting y = 0, and when we simplify, we get ax + b = 0, or $x = \frac{-b}{a} $.

### Finding Zeros for Quadratic Equations

A **quadratic equation** can be factored in by using either of the two methods. It is possible to factor the **quadratic equation** of the type $x^{2} + x(a + b) + ab = 0$ as (x + a)(x + b) = 0, with the polynomial’s zeros being x = -a and x = -b.

And since the zeros in a **quadratic equation** of the type $ax^{2}+ bx + c = 0$ cannot be factorised, the formula approach can be used to get the zeros is $ x = \frac {[-b \pm \sqrt{(b^{2}-4ac)}]}{2a}$.

### Finding Zeros for Cubic Equations

By using the **remainder theorem**, the **cubic equation **of the form $y = ax^{3} + bx^{2} + cx + d$ can be factorized. The variable x = $\alpha$ can be replaced with any lower values according to the remainder theorem, and if the value of y results in **zero**, y = 0, then the (x – $\alpha$ ) is one root of the equation.

We can divide the **cubic equation** by $(x – \alpha )$ using **long division to create a quadratic equation**.

The quadratic equation can finally be solved using either the formula approach or **factorization **to achieve the required two roots for the quadratic equation.

### Finding Zeros for Higher Degree Polynomials

**Higher degree polynomials** can be factorized using the remainder theorem to create a quadratic function. Higher degree polynomials are generally represented as $y = ax^{n}+ bx^{n-1}+cx^{n-2} + ….. px + q$.

After calculating the quadratic formula from these **higher-degree polynomials,** they can be factorized to obtain the roots of the equation.

## What Is a Multiplicity of Polynomial?

The** multiplicity** of a polynomial means the number of times the **root** values appear in a polynomial equation. If we have the factored version of the polynomial, figuring out the number of roots is simple. Alternately, it is also feasible to ascertain the number of roots by examining the polynomial graph.

The $x$-intercepts of the polynomial’s graph are the real roots of the polynomial. As a result, we can learn how many real roots it has by examining a polynomial graph.

Similarly, by examining the polynomial’s **zeros** or its factored form, we may predict how often the graph will touch or cross the x-axis. The **multiplicity** of a **zero** or a root is the number of times its related factor appears in the polynomial.

For example, a quadratic equation (x+5)(x-3) has the root x= -5 and x = 3. This explains that the line of the equation passes through x= -5 and x = 3 once.

If the **polynomial** is not factored in, we must factor it or obtain a graph of the polynomial to examine how it behaves while crossing or contacting the x-axis.

## Solved Examples

The **Multiplicity Calculator** is an efficient way to calculate the zeros or roots of a polynomial equation.

Here are some solved examples that are solved using a **Multiplicity Calculator**.

### Solved Example 1

A high school student is given the following polynomial equation:

\[ 3x^{2} – 6x \]

The student must figure out the **zeros** and create a graph using this polynomial equation. Find the **zeros** and plot a graph using the polynomial equation.

### Solution

Using the **Multiplicity Calculator,** we can calculate the **zeros** of the polynomial equation and plot a graph. First, we enter the polynomial equation into the **Multiplicity Calculator**.

After entering the polynomial equation, we click the “Submit” button on the **Multiplicity Calculator.** The calculator opens a new window and displays the results of our equation.

The results from the **Multiplicity Calculator** are given below:

Input interpretation:

\[ Roots \ 3x^{2} – 6x = 0 \]

Results:

**x = 0**

**x = 2**

Root Plot:

Figure 1

Number Line:

Figure 2

Sum of Roots:

**2**

Product of Roots:

### Solved Example 2

While researching, a mathematician comes across a **higher degree polynomial** equation $y = x(x+1)^{2}(x+2)^{3}$. To complete his research, the mathematician needs to find the **roots** of the polynomial equation.

Find the **roots** of the higher degree polynomial.

### Solution

To solve the equation and find the roots by using the **Multiplicity Calculator, **first we plug in the polynomial equation we are provided into its respective input box.

After plugging in the polynomial equation, all we need to do is click the “Submit” button on the **Multiplicity Calculator**. The **Multiplicity Calculator** instantly provides the result for the polynomial equation.

The following are the results calculated by the **Multiplicity Calculator**:

Input interpretation:

\[ Roots \ x(x+1)^{2}(x+2)^{3} = 0 \]

Results:

**x = -2 (multiplicity 3)**

**x = -1 (multiplicity 2)**

**x = 0 (multiplicity 1)**

Root plot:

Figure 3

Number Line:

Figure 4

Sum of Roots:

**-8**

Product of Roots:

### Solved Example 3

While working on an assignment, a college student stumbled upon the following equation:

\[ y = \frac{1}{6} (x-1)^{3}(x+3)(x+2) \]

The student must find the **multiplicity** of zeros in the polynomial equation. Find the **multiplicity** of zeros of the polynomial equation given.

### Solution

We can use the **Multiplicity Calculator** to find the **multiplicity** of zeros of the polynomial equation**.** To use the calculator, we first add the polynomial equation in the input box.

After adding the polynomial equation into the **Multiplicity Calculator,** we click the “Submit” button and let the calculator do its job. The **Multiplicity Calculator** provides us with the **roots** of the polynomial equation in a fraction of a second.

The results of the **Multiplicity Calculator** are given below:

Input Interpretation:

\[ Roots \ \frac{1}{6} (x-1)^{3}(x+3)(x+2) = 0 \]

Results:

**x = -3 (multiplicity 3)**

**x = -2 (multiplicity 2)**

**x = 1 (multiplicity 1)**

Root plot:

Figure 5

Number Line:

Figure 6

Sum of Roots:

**-2**

Product of Roots:

**6**

### Solved Example 4

Consider the following polynomial equation:

\[ ( x + 3 ) ( x – 2 )^{2} ( x + 1 )^{3} \]

Using the equation above, calculate the **multiplicity of zeros**.

### Solution

The **Multiplicity Calculator** can be used to find the multiplicity of zeros in the polynomial equation we are provided. To use the calculator, we enter the polynomial equation first.

Once we enter the polynomial equation, we click the “Submit” button on the **Multiplicity Calculator**.

The Multiplicity Calculator gives us the following results:

Input interpretation:

\[ Roots \ ( x + 3 ) ( x – 2 )^{2} ( x + 1 )^{3} = 0 \]

Results:

**x = -3 (multiplicity 3)**

**x = -1 (multiplicity 2)**

**x = 2 (multiplicity 1)**

Root plot:

Figure 7

Number Line:

Figure 8

Sum of Roots:

**-2**

Product of Roots:

**12**

*All images/graphs are created using GeoGebra.*

#### Math Calculators List

## FAQs

### What math calculator shows steps? ›

**Algebra Calculator** is a calculator that gives step-by-step help on algebra problems.

**What is the website that solves any math problem? ›**

**QuickMath** will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

**How can I get math answers online? ›**

You'll find hundreds of instant-answer, self-help, math solvers, ready to provide you with instant help on your math problem. **Webmath is a math-help web site that generates answers to specific math questions and problems, as entered by a user, at any particular moment**.

**What is the most accurate calculator? ›**

Best Overall: **Texas Instruments TI-36X Pro Engineering/Scientific Calculator**. The Texas Instruments TI-36X features a MultiView display area that shows four lines (most other calculators just show one or two lines) and multiple calculations on the screen at the same time.

**How do you solve equations step-by-step? ›**

Algebra - How To Solve Equations Quickly! - YouTube

**What is the best math solver app? ›**

**Best Math Solver Apps for Android and iPhone**

- Photomath - Camera Calculator. (Android, iPhone, iPad) ...
- Mathway. (Android, iPhone, iPad) ...
- CameraMath - Homework Help. (Android, iPhone, iPad) ...
- Geometry solver ² (iPhone, iPad) ...
- Maple Calculator: Math Helper. Android iOS. ...
- WolframAlpha. ...
- MyScript Calculator. ...
- Microsoft Math Solver.

**Is there a website that solves math problems with steps for free? ›**

4. **Cymath**. Cymath is a free application that gives a step-by-step solution to any math problem.

**What is the best website to solve math problems for free? ›**

Photomath—scan and solve math problems. **Khan Academy**. Math Brain Booster Games. Mathway—Math problem solver Mathway on Google Play or Mathway on Apple.

**Is there a free version of Mathway? ›**

**The basic Mathway app, which lets you solve problems using its virtual calculators, is free**. If you want to see the steps that go into solving the problems, you have to pay.

**Can Google solve math problems? ›**

**Google Lens**

It can recognize anything you take pictures of, including math problems. Open the Google App on your phone and tap the camera icon in the search bar. Next, select Homework at the bottom of the screen. Then, just snap a picture of a math problem for an instant answer.

### Where can I ask math questions and get answers? ›

**Ask an Expert**

- Ask Dr. Math - This is probably the best resource out there for anyone wanting an answer to a math question. ...
- Ask MathNerds.com - A large group of math experts have banded together to provide this excellent service. ...
- Gomath.com - This site has tutors available to answer your math questions for free.

**What is the most powerful calculator online? ›**

**The 6 Best Online Scientific Calculators**

- web2. 0calc.
- Desmos Graphing Calculator.
- Good Calculators.
- Symbolab.
- WolframAlpha.
- Calculator.net.

**What is the most advanced calculator? ›**

The **TI-NSpire by Texas Instruments** is arguably the most powerful and reliable calculator you can buy. The two different types of TI-NSpire—the CX II and the CX II CAS—are both great options for math students handling coursework or about to tackle national exams (SATs and ACTs).

**Which calculator is best for students? ›**

**10 Best Scientific Calculators for College Students**

- Casio FX-991ESPLUS Scientific Calculator.
- Casio fx-300ESPLS2 2nd Edition Scientific Calculator.
- Sharp EL-W516TBSL 16-Digit Advanced Scientific Calculator.
- Casio fx-115ESPLS2 White Advanced Scientific Calculator with Natural Display.

**How do you solve multi-step problems? ›**

Multi-Step Word Problems - YouTube

**How do you check answer in multi-step equations? ›**

To solve multi-step equations with fractions, you can multiply each term by the least common denominator to eliminate the fractions first. To check the solution, simply **substitute the value into the variable to see if the equation is true**.

**How do you solve multi-step equations word problems? ›**

Multi-Step Equation Word Problems - YouTube

**Is there an app that solves any math problem? ›**

Meet Microsoft Math Solver, an all-in-one app that helps with a wide range of mathematical concepts–from elementary arithmetic and quadratic equations to calculus and statistics. All you need to do is use your smartphone camera to click a photo of a math problem to solve it–be it handwritten or printed.

**Is there a calculator that can solve any problem? ›**

More than just a calculator. Calculator All-In-One can help you solve math homework assignments, check answers, and solve multiple questions with just.

**What is the best free app for math? ›**

**10 Free Math Apps for Students that Teachers Swear By**

- Prodigy Game. Meant for students of grades 1-8, Prodigy Game is available for free on iOS, Android and web platforms. ...
- Math Training for Kids. ...
- CK12. ...
- Colorado's PhET. ...
- Photomath. ...
- Khan Academy. ...
- GeometryPad. ...
- BuzzMath.

### Can Photomath do word problems? ›

**Photomath currently solves word problems for a limited number of textbooks under our Photomath Plus subscription**, but we're working hard every day to add more to our library. We recommend enabling notifications from us so that you'll know when we add new content!

**Can Cymath solve word problems? ›**

**Yes, Cymath can solve all math word problems**. It's quick and intuitive and consists of a vast library of solutions to math problems.

**Can I take a picture of a math problem and get answer? ›**

Open the Google App on your phone and tap the camera icon in the search bar. Next, select Homework at the bottom of the screen. Then, just snap a picture of a math problem for an instant answer. **Photomath is the king of math solving apps.**

**Is Microsoft Math Solver free? ›**

**It is absolutely FREE** and NO ads! Contact us at mathsupport@microsoft.com or tweet us at @microsoftmath We look forward to your feedback.

**How do you solve math problems quickly? ›**

**Here are four steps to help solve any math problems easily:**

- Read carefully, understand, and identify the type of problem. ...
- Draw and review your problem. ...
- Develop the plan to solve it. ...
- Solve the problem.

**What is Mathwarehouse? ›**

Mathwarehouse.com--**a website dedicated to Math lessons, demonstrations, interactive activities and online quizzes on all areas of geometry, algebra and trigonometry**.

**What app is better than Mathway? ›**

The best alternative is **SpeedCrunch**, which is both free and Open Source. Other great apps like Mathway are Wolfram Alpha, SageMath, Symbolab Math Solver and fxSolver. Mathway provides students with the tools they need to solve their math problems.

**What can I use instead of Mathway? ›**

**Websites like Mathway**

- Microsoft Math Solver. (Android, iPhone, iPad) ...
- Quick Math. (iPhone, iPad) ...
- WebMath. (Website) ...
- Symbolab Calculator. (Android, iPhone, iPad) ...
- Cymath - Math Problem Solver. (Android, iPhone, iPad) ...
- WolframAlpha. (Android, iPhone, iPad) ...
- MathPapa - Algebra Calculator & Equation Solver App. (Android, iPhone, iPad)

**How accurate is Mathway? ›**

Mathway offers **quick and accurate answers to the mathematical problems you input** and can work offline, being a useful app to have at school. While extremely good at providing answers, this app won't show you how it solved a problem unless you buy a monthly or annual subscription.

**What tool Google helps us solve math problems? ›**

Now, in light of the current crisis, Google has added a 'Homework' filter into Lens to help with Math problems. Using this tool, you (or your child) can scan a math equation/problem and have it directly solved.

### How can I solve my problem? ›

**Six step guide to help you solve problems**

- Step 1: Identify and define the problem. State the problem as clearly as possible. ...
- Step 2: Generate possible solutions. ...
- Step 3: Evaluate alternatives. ...
- Step 4: Decide on a solution. ...
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- Step 6: Evaluate the outcome.

**How do you solve math problems with Iphone? ›**

Use Your iPhone or iPad Camera to Solve Math Problems Instantly [How ...

**Where can I get free answers? ›**

**Answers**

- Answers.com. User-powered question and answer platform. ...
- Ask a Librarian. Online reference desk service from the Library of Congress. ...
- Brainly. Post questions to a community of millions of students and teachers. ...
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**Which app is best for question and answer? ›**

**Download Questions And Answers - Best Software & Apps**

- PhotoMath. 7.5.1. 4.3. ...
- Quora Ask Questions Get Answers. 3.0.32. 4.2. ...
- Triviador World. varies-with-device. (4 votes) ...
- Medscape. 10.3.0. 4.3. ...
- Socratic - Homework answers. 1.8.1. (4 votes) ...
- Happy Couple - love quiz. 1.9. (1 vote) ...
- Answer - Ask Questions Doubts. 4.6.1. ...
- Apple Support. 4.3.1.

**Where can I ask a question for free? ›**

**Where can I ask a question on the Internet?**

- Answerbag. Answerbag is a website that helps answer questions in almost all types of different categories. ...
- Answers.com. ...
- Ask Me Help Desk. ...
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- Brilliant.org.

**Can I get IXL for free? ›**

**Yes, IXL offers a free app for students to practice skills and earn awards on an iPad or iPhone**! If you are using an iPad, there's even a scratchpad to work out problems right on the screen—no paper needed.

**Is brilliant free? ›**

**Brilliant provides a daily challenge that is free to complete**. If you enjoy these you can take the 7 day free trial of Brilliant Premium. After that, if you want to continue to use the Platform you need to subscribe. At the time of writing you could do this on a monthly basis at $24.99 per month.

**Is Khan Academy enough for math? ›**

Khan Academy math is an online math curriculum or supplement. There are videos, practice problems, and mastery challenges available to help teach math concepts. Is Khan Academy good for math? The program is pretty comprehensive, so in general, **yes it is good for math**.

**What is a good online calculator? ›**

1. **Desmos**. Desmos is an advanced online scientific calculator. It features a tabbed user interface with buttons for making calculations in degrees and radians, angles, pie values, percentages, powers, and round numbers.

**What does E mean in maths? ›**

**Euler's Number** 'e' is a numerical constant used in mathematical calculations. The value of e is 2.718281828459045…so on. Just like pi(π), e is also an irrational number.

### What kind of calculator does a 6th grader need? ›

The Ohio Department of Education recommends **scientific calculators** for the grades 6-8 tests, but students may use calculators with lower functionality.

**What kind of calculator do I need for 11th grade? ›**

The **Texas Instruments TI-36X** is one of the most popular high school calculators. The best part is that the calculator is approved for many exams, which is why it will get you through almost all of your high school. The best use of this calculator is for algebra, engineering, calculus, physics, geometry, and statistics.

**What type of calculator is used in high school? ›**

**Scientific calculators** are designed for higher level math and science calculations. These are often required in middle-school and high-school classes.

**What kind of calculator do I need for 9th grade? ›**

Priced at roughly $125, the **TI-84 Plus CE Graphics Calculator** is an ideal choice for many grades 9 students. And there you have it. Three of the top calculators on the market today for grade 9 students.

**What calculator can solve anything? ›**

More than just a calculator. Calculator All-In-One can help you solve math homework assignments, check answers, and solve multiple questions with just.

**Is there a calculator that solves algebra? ›**

**Texas Instruments Nspire CX II CAS Graphing Calculator**

Nspire CX II CAS is one of the top calculators that allow you to explore symbolic algebra and symbolic calculus in addition to standard numerical calculations. It is a great tool for doing step-by-step arithmetic, algebraic and calculus calculations.

**What is algebraic proof? ›**

An algebraic proof **shows the logical arguments behind an algebraic solution**. You are given a problem to solve, and sometimes its solution. If you are given the problem and its solution, then your job is to prove that the solution is right.

**How do you use a scientific calculator for basic math? ›**

How to Use Your Scientific Calculator - YouTube

**Can Google solve math problems? ›**

**Google Lens**

It can recognize anything you take pictures of, including math problems. Open the Google App on your phone and tap the camera icon in the search bar. Next, select Homework at the bottom of the screen. Then, just snap a picture of a math problem for an instant answer.

**Is Mathway free? ›**

Show Your Work. **The basic Mathway app, which lets you solve problems using its virtual calculators, is free**. If you want to see the steps that go into solving the problems, you have to pay. Upgrading to the paid version costs either a $19.99 monthly subscription or $79.99 per year.

### Who invented math? ›

The earliest evidence of written mathematics dates back to the **ancient Sumerians**, who built the earliest civilization in Mesopotamia. They developed a complex system of metrology from 3000 BC.

**Is Microsoft Math Solver free? ›**

**It is absolutely FREE** and NO ads! Contact us at mathsupport@microsoft.com or tweet us at @microsoftmath We look forward to your feedback.

**Is there a physical calculator like Mathway? ›**

**MathPapa - Algebra Calculator & Equation Solver App**. MathPapa is a calculator like Mathway for solving algebra problems that you will find anywhere.

**Can you get Photomath on a calculator? ›**

One of the best math solving apps, Photomath Camera Calculator uses augmented reality, which means that you can simply point your camera at any piece of paper with an equation or an arithmetic problem and it will find a solution. **Photomath Camera Calculator is free to download for iOS and Android devices**.

**What are the three types of proofs? ›**

There are many different ways to go about proving something, we'll discuss 3 methods: **direct proof, proof by contradiction, proof by induction**.

**How do you answer a math proof question? ›**

Proving Identities and proofs in general | ExamSolutions - YouTube

**How do I use my scientific calculator on my phone? ›**

To open the Scientific calculator, **tap the Menu icon (at the upper-right corner of the screen), then tap Scientific calculator**. To return to the Basic calculator, tap the Menu icon (at the upper-right corner of the screen), then tap Basic calculator.

**What is E in calculator? ›**

What does E mean on a calculator? From: A Maths Dictionary for Kids by Jenny Eather at www.amathsdictionaryforkids.com If a number is too big or too small to fit in a calculator display, often, scientific notation using the letter E (or e) for **exponent (power or index)** will be used.

**Why do calculators give different answers? ›**

**The difference has something to do with the mode or the program of the calculator**. For one, not all calculators follow the order-of-operations hierarchy, which leads to a different interpretation of the equation. In this case, the true form of the equation is 6/2(2+1), which yields 9.