Polynomials | Algebra

Casus irreducibilis

In algebra, casus irreducibilis (Latin for "the irreducible case") is one of the cases that may arise in solving polynomials of degree 3 or higher with integer coefficients algebraically (as opposed to numerically), i.e., by obtaining roots that are expressed with radicals. It shows that many algebraic numbers are real-valued but cannot be expressed in radicals without introducing complex numbers. The most notable occurrence of casus irreducibilis is in the case of cubic polynomials that have three real roots, which was proven by Pierre Wantzel in 1843.One can see whether a given cubic polynomial is in so-called casus irreducibilis by looking at the discriminant, via Cardano's formula. (Wikipedia).

Video thumbnail

500 years of NOT teaching THE CUBIC FORMULA. What is it they think you can't handle?

Why is it that, unlike with the quadratic formula, nobody teaches the cubic formula? After all, they do lots of polynomial torturing in schools and the discovery of the cubic formula is considered to be one of the milestones in the history of mathematics. It's all a bit of a mystery and ou

From playlist Recent videos

Video thumbnail

The BuShou of HanZi :力

A brief description of the BuShou of 力.

From playlist The BuShou of HanZi

Video thumbnail

What Lives In Cheese?

What makes cheese so delicious? It's the bacteria, fungi, mites, and maggots living in it, of course! Subscribe! http://bit.ly/1FkxVLb ‖ Twitter! https://twitter.com/gross_science ‖ Tumblr! http://grossscience.tumblr.com/ ↓Want more info?↓ The Wolfe Lab at Tufts University https://sites.t

From playlist Gross Science

Video thumbnail

The BuShou of HanZi :手

A brief description of the BuShou of 手.

From playlist The BuShou of HanZi

Video thumbnail

The BuShou of HanZi :耳

A brief description of the BuShou of 耳.

From playlist The BuShou of HanZi

Video thumbnail

The BuShou of HanZi :囗

A brief description of the BuShou of 囗.

From playlist The BuShou of HanZi

Video thumbnail

The BuShou of HanZi :宀

A brief description of the BuShou of 宀.

From playlist The BuShou of HanZi

Video thumbnail

The BuShou of HanZi :禾

A brief description of the BuShou of 禾.

From playlist The BuShou of HanZi

Video thumbnail

Human Tissue Experiments on the ISS Could Advance 3D Printed Organs

Seeker host Maren Hunsberger sits down with NASA Scientist Dr. Liz Warren to talk about the amazing science happening on the ISS, why microgravity is the ideal condition for health experiments, and how this all might lead to 3D printed body parts. SpaceX Sent Algae to the ISS, Here's How

From playlist Elements | Season 4 | Seeker

Video thumbnail

There’s an Artificially Intelligent Crew Member on the ISS… Wait What? (Part 3 of 3)

Cutting-edge technology is used every day on the ISS, including an artificially intelligent robot assistant. What else are we experimenting with up there? Part 1 of 3 - https://youtu.be/AFZqgKshU3U Part 2 of 3 - https://youtu.be/4U5UWSFD5D4 Read More: Floating robot Cimon sent to

From playlist Seeker Plus

Video thumbnail

GRCon19 - Demonstration of GNU Radio Compatibility with a NASA Space... by David Miller

Demonstration of GNU Radio Compatibility with a NASA Space Communications Network Modem by David Miller This paper presents the results of testing that the author recently conducted to demonstrate that a GNU Radio Software Defined Radio (SDR) receiver is compatible with a typical National

From playlist GRCon 2019

Video thumbnail

Pair of Monster Black Holes in a Peculiar Galaxy Just Broke a Few Records

Good telescope that I've used to learn the basics: https://amzn.to/35r1jAk Get a Wonderful Person shirt: https://teespring.com/stores/whatdamath Alternatively, PayPal donations can be sent here: http://paypal.me/whatdamath Hello and welcome! My name is Anton and in this video, we will tal

From playlist Galaxies, Quasars, Blazars

Video thumbnail

Microgravity on the ISS Makes for a Perfect Lab, Here’s Everything We're Learning (Part 1 of 3)

Fish, mice, and worms have joined astronauts in space to be part CASIS’s mission to understand the effects of microgravity on the ISS. Join us in talking to Dr. Mike Roberts to learn more! Part 2 of 3 - https://youtu.be/4U5UWSFD5D4 Part 3 of 3 - https://youtu.be/vMzRzR6qi44 Get 20% off

From playlist Seeker Plus

Video thumbnail

Empires, Pirates, and Jenkins' ear

Sponsored by Blinkist. The first 100 people who go to https://www.blinkist.com/thehistoryguy are going to get unlimited access for one week to try it out. You'll also get 25% off if you want the full membership. On this date, April 9, 1731, a war, which came as the result of a war which

From playlist Great Britain

Video thumbnail

Alexander Schrijver: The partially disjoint paths problem

Abstract: The partially disjoint paths problem asks for paths P1,…,Pk between given pairs of terminals, while certain pairs of paths Pi,Pj are required to be disjoint. With the help of combinatorial group theory, we show that, for fixed k, this problem can be solved in polynomial time for

From playlist Control Theory and Optimization

Video thumbnail

The BuShou of HanZi :目

A brief description of the BuShou of 目.

From playlist The BuShou of HanZi

Video thumbnail

The BuShou of HanZi : 車

A brief description of the BuShou of 車.

From playlist The BuShou of HanZi

Video thumbnail

Franklin D. Roosevelt and the Democratic Party

In this lecture, Professor Iwan Morgan (University College London) thinks about the transformation of the Democratic Party between 1933-45, focusing in particular on: (i) the party’s relative lack of electoral success in the decades prior to Roosevelt; (ii) the Democratic Party’s tradition

From playlist History

Video thumbnail

The BuShou of HanZi :齒

A brief description of the BuShou of 齒.

From playlist The BuShou of HanZi

Video thumbnail

The BuShou of HanZi :刀

A brief description of the BuShou of 刀.

From playlist The BuShou of HanZi

Related pages

Quadratic formula | Quintic function | Trigonometry | Polynomial long division | Imaginary number | Imaginary unit | Algebra | Angle trisection | Formally real field | Discriminant | Splitting field | Field extension | List of trigonometric identities | Monic polynomial | Integer | Algebraic function | Square-free polynomial | Nth root | Complex conjugate | Galois group | Tschirnhaus transformation | Trinomial | Pierre Wantzel | Cubic equation | Ordered field | Conjugate element (field theory) | Constructible number