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

The cubic equation is mostly a waste of time. In my work, I've used the quadratic many times, but any higher orders are done numerically. I've never needed to solve a cubic exactly, and if I did, I could look it up. It's not the sort of thing we should waste time teaching. The real reason we shouldn't teach it is that students could be learning much more important math — probability and statistics, mortgages and interest rates, etc. What about vector spaces and matrix algebra? Why spend time on the cubic equation? It isn't worth it.

Fascinating. I am really impressed. You explained it to the comprehension of a junior High school level student. I was already aware of all these tricks you applied but never accord to me to put them together the way you did. I thank you for your excellent demonstration.

I have this equation 8y^3 – 4y + 1 = 0 and know that one root is y = (√5 – 1)/4 or 1/(√5 + 1) = 1/(2Φ) = sin18°, where Φ = (√5 + 1)/2 is the Golden Ratio. I'm going to see if this formula gives the solution in one of these forms.

I use the fact that every cubic equation with real coefficients has at least one real root. Quickly graphing the function I estimate one real root and use Newton-Raphson iteration to increase its accuracy as necessary. Then I use synthetic division to obtain the factored quadratic equation and the quadratic formula to obtain the other two roots. Why on earth would I ever memorize such a messy equation when I rarely find roots of a cubic equation and a much simpler iterative method exists? That formula might be useful for writing a computer program to diagonalize 3 by 3 inertia matrices.

We are waiting for the Galois theory.

you r great sir.
reveals secrets of maths formule
i like you sir.

doubt: whats the point of turning b into zero like you have now bounded yourself to solve a certain type of cubic which doesnt not consist of term x^2. the removing a was good and works for all

because the cubic formula takes up 4 pages in my handbook of mathematical functions

If you want to find the other two cube roots, there's an easy way to do so:

After solving a cubic of the form [ x^3 + px + q = 0 ], take the solution acquired from plugging into the cubic formula, which we'll call "k", and create the quadratic [ x^2 - kx + q/k = 0 ].

If the original cubic has one real solution, then the new quadratic will have two complex solutions.
If the original cubic has two real solutions, then the new quadratic will have one real solution.
If the original cubic has three real solutions, then the new quadratic will have two real solutions.

You can then plug in the acquired values for x in the original cubic, and the math will work out just fine.

The Missed link in Maths. New High-Order Numerical Methods: /6lORU03yuvY The Fifth Arithmetical Operation. The Missed Link in Mathematics: /VKy0UPOf1Ew
Dynamic Maths. The Wonders of Number /J6k_O6i74fw The missed link that the employees and brainwashed slaves of the current vicious educational system do not want you to see, because they want you to be slaved forever: /jM9KZjgnujA

Great video ❤

I love the little detail of his shirt.
When he talks about the quadratic formula he wears a shirt with a "square root" and then when he starts talking about the cubic formula he changes to a shirt with a "cube root".

Neat trick with the shirts

I wonder, what happens, if p = 0, and the inflection point lies right on the x-axis 🤔.

What second derivative represents graficly

learned Cardano and Ferrari formulas in 8th grade in advanced math class. Definitely something absolutely unnecessary for an average mid school student.

The `x^2 + A = 0` thing is a great illustration that all parabolas are geometrically similar.

I dont think, in India, we had not studied.
I remember, studing of
standard equation, x^3+3mx-2n=0
which has one definite real root, and two other conjugates, either real or imaginary depending on some condition
real root : (m+d)^1/3+(m-d)^1/3 where d^2=m^3+n^2

whatever, there are many things , new and crazy from your videos
quiet interesting
especially, finding next prime number, a way to write an algorithm
checking it to impleent.
really intersting

I've never understood the fetish for writing solutions in terms of radicals or even elementary functions. Fine, maybe before computers it was important because we had more efficient tricks to approximate these functions at our fingertips but just using Newton's method (or better computational approximations) is no less a solution (you can prove convergence for these roots if you start near enough root).

At the end of the day, formally speaking, a converging sequence is closer to the definition of a real than a formula using roots (hell here we even get a sigma1 definable converging sequence with computably boundable errors).

IMO this reinforces the wrongheaded idea that math is just about memorizing a bunch of formulas and tricks. Hell, I think it's silly even to teach the quadratic formula in the modern world. Plugging into a formula is no different than plugging into a calculator.

Teach completing the square as a technique and if someone needs to understand it they can rederive, if they don't they can use a calculator.

wow....i have never seen/met this type of teacher...amazing

My math teachers taught it. Circa 2008 or 9.

I feel so ashamed of myself

Wonderful, many thanks !

With no intention to annoy anyone. Math, physics chemistry logic, ethimology , anatomy and agriculture, are some of the subjects which should be taught from the kindergarden... However, hiw the actual education system works is to make the children and people in general dumber... But why? For those who wish to learn more about why is the Educational system failing. I sugest the book Rockefeller Medicine Man .

I have an AI doing it for me I don't have to learn this junk

Fun fact: In Brazil we refer to it as "Bhaskara's formula" (in Portuguese "Fórmula de Bhaskara") due to a misunderstanding when the formula arrived here, so that we thought that formula was invented by an Indian called Bhaskara, but he only idealized it without an algebrac notation.

perfect t-shirt for the topic :)

Question: The cubic polynomial in fun fact number one, must be monic?

You are so awesome dude! ❤

your completing the square explanation was the most clear and concise one I've ever seen!

i can't believe such a perfect video exists... going into detail but still understandable. thank you very much

I like the cube roots on your tee-shirt

my teacher told us about this in year 11, but I think I was the only one to chase it up

There are other, better, and far more useful things that could be taught in the time that this useless bit of trivia might fill. How about statistical tests, or a better understanding of probability and conditional probability? The idea of bothering with this is probably the least intelligent/most worthless idea I’ve seen in quite some time.

When they attempted to teach me how to calculate the square root of a number, they used the algebraic method. It gets more difficult for each digit. And if you make a mistake, all the subsequent work is wasted.
Newton's method is simpler. More understandable. Converges much more rapidly (the number of digits of accuracy doubles each iteration). Guess the answer. Then divide the number by your guess. One number is greater than the square root. The other number is less than the square root. Average them. This is your new guess.
No pulling down two digits. Doubling the divisor and subtracting. Just to get one more digit.
Why are these piss-poor algorithms still taught in school?

Then Trig walked in...

🫐🍡➕🍒🥢➕🥑➕🧃= 🍽️ *Hint🤤

There is a much easier method to solve the quartic equation which we were taught, which was take for example x^4 = t^2 then x^2 = t and using this substitution we can solve the quartic like a quadratic and again put values of t to get x