Mathematician Finds Easier Way to Solve Quadratic Equations

[Gerson W. Barbosa]

(04-23-2024 08:36 PM)Maximilian Hohmann Wrote:  Hello!

(04-23-2024 07:20 PM)rprosperi Wrote:  This article apparently first ran in Popular Mechanics... who knew to look there for math news??

Let the doubters and defenders come forth and critique....

The YouTube video linked in the article is four years old and we haven't heard of this "easy" method ever since. So my conclusion is, that Mr. Darwin's principle took care of it ;-)
But really I find it hard to understand what he is explaining there and how his method would work so easily with non-integer factors.

Indeed he doesn’t explain it step by step. Hopefully, the following is easier to understand:

x² + b.x + c = 0

x₁ + x₂ = -b

x₁.x₂ = c

u = (x₁ + x₂)/2 = -b/2

=>

x₁ = -b/2 - u (1)

x₂ = -b/2 + u (2)

and

x₁.x₂ = c
(-b/2 - u)(-b/2 + u) = c

or, from the difference of squares formula,

(-b/2)² - u² = c
u² = (-b/2)² - c
u = √((-b/2)² - c)

Then, from (1) and (2) above:

x₁ = -b/2 - √((-b/2)² - c)

x₂ = -b/2 + √((-b/2)² - c)

Regards,

Gerson.