Solving Polynomial Equations with Mathematica & the Wolfram Language

Mathematica Essentials - the first PRO COURSE from Socratica

Learn along with free Mathematica notebooks available on github:

You may have memorized the formula to solve quadratic equations. You may have seen the formula for cubic equations, or even quartic equations (although most people don't memorize these).
But what about polynomial equations of higher degree?
And can we use MATHEMATICA to solve these equations?

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MATHEMATICA ESSENTIALS by Socratica
Polynomial Equations

0:00 Introduction to the Solve function
0:51 Solving linear equations
2:16 Solving quadratic equations
3:13 Solving cubic equations
3:48 Solving quartic equations
4:31 Quintic and higher equations
5:44 Example 1 (cubic)
7:11 Example 2 (quartic)
7:32 Example 3 (6th degree)

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We recommend the following (affiliate links):
The Wolfram Language

The Mythical Man Month - Essays on Software Engineering & Project Management

Innumeracy: Mathematical Illiteracy and Its Consequences

Mindset by Carol Dweck

How to Be a Great Student (our first book!)

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If you find our work at Socratica valuable, please consider becoming our Patron on Patreon!

If you would prefer to make a one-time donation, you can also use
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Written & Produced by Michael Harrison & Kimberly Hatch Harrison
Edited by Megi Shuke

About our Instructors:

Michael earned his BS in Math from Caltech, and did his graduate work in Math at UC Berkeley and University of Washington, specializing in Number Theory. A self-taught programmer, Michael taught both Math and Computer Programming at the college level. He applied this knowledge as a financial analyst (quant) and as a programmer at Google.

Kimberly earned her BS in Biology and another BS in English at Caltech. She did her graduate work in Molecular Biology at Princeton, specializing in Immunology and Neurobiology. Kimberly spent 16+ years as a research scientist and a dozen years as a biology and chemistry instructor.

Michael and Kimberly Harrison co-founded Socratica.
Their mission? To create the education of the future.

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PLAYLISTS

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#Mathematica #Wolfram #WolframLanguage

[Socratica]

Mathematica Essentials - the first PRO COURSE from Socratica

[michaelzumpano]

This is the first of your Mathematica videos I’ve seen. Very clear and focused. Mathematica is an incredibly complex ecosystem. You probably need no other language. I started using it about 25 years ago. I took a week of classes in 2004 and became pretty proficient in their functional programming language. But lately I’ve been using packages in Python because (hand wavy)… it’s a more common denominator for things like AI and sparse solutions. Can you tell me if Mathematica has a connector or Python packages for licensed users, or am I speaking heresy?

[the_larsonfamily]

While there is no general formula for solving a quintic equation, some can be solved using methods such as radicals and special functions. However, for most quintic equations, numerical methods like the Durand-Kerner method or the Jenkins-Traub algorithm are used to find approximate solutions. #quinticequation #math

[cybervigilante]

My real problem with Mathematica is pattern matching, which goes all through it but can be Very obscure and hard to work at times.

[kirbymarchbarcena]

Gotta say...looking at the formulae can be scary for those unfamiliar