Uploaded April 2023 | Updated September 2026, 2 weeks ago
Here's the complete derivation of the cubic formula for ax^3+bx^2+cx+d=0. We will first review the formula for the quadratic equation x^2+px+q=0. Then we will take three main steps to solve the cubic equation. This ultra-algebra proof is a must-see for any math enthusiast looking to expand their knowledge and deepen their understanding of the roots of cubic equations. See my Patreon for my hand-written notes: patreon.com/posts/notes-on-cubic-81794694
de Moivre quintic formula ๐ youtu.be/L8W684pCHyc
0:00 we will derive the cubic formula
0:07 review on solving the quadratic equation x^2+px+q=0 and the pq-formula
6:17 part1, get rid of the x^2 term in the y-world (let x=y-b/(3a))
17:23 part 2, solving y^3+py+q=0 (let y=z-p/(3z))
39:27 part 3, put everything together
#maths #imaginarynumber #blackpenredpen
๐ Shop math t-shirts & hoodies: blackpenredpen.creator-spring.com
10% off with the code "WELCOME10"
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๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt bbaa Joash Hall
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Thank you all!
Here's the complete derivation of the cubic formula for ax^3+bx^2+cx+d=0. We will first review the formula for the quadratic equation x^2+px+q=0. Then we will take three main steps to solve the cubic equation. This ultra-algebra proof is a must-see for any math enthusiast looking to expand their knowledge and deepen their understanding of the roots of cubic equations. See my Patreon for my hand-written notes: patreon.com/posts/notes-on-cubic-81794694
de Moivre quintic formula ๐ youtu.be/L8W684pCHyc
0:00 we will derive the cubic formula
0:07 review on solving the quadratic equation x^2+px+q=0 and the pq-formula
6:17 part1, get rid of the x^2 term in the y-world (let x=y-b/(3a))
17:23 part 2, solving y^3+py+q=0 (let y=z-p/(3z))
39:27 part 3, put everything together
#maths #imaginarynumber #blackpenredpen
๐ Shop math t-shirts & hoodies: blackpenredpen.creator-spring.com
10% off with the code "WELCOME10"
----------------------------------------
๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt bbaa Joash Hall
----------------------------------------
Thank you all!
