I thought this was a cool find. Quadratic equations generally have at most two places where they intersect the x-axis (their roots). Math professor Po-Shen Loh figured that between the two roots there must be a number, and he solves for that number and uses it to find the roots.
https://www.technologyreview.com/s/6147 ... ions-easy/
Basically, the end result is instead of memorizing a single complicated formula, you can memorize two simpler ones (the upshot is that instead of entering two calculations into your calculator like you do with the quadratic formula, you just have to enter one).
Suppose you have the following quadratic equation:
x^2 + Bx + C = 0. (we've divided A out already)
The old way to solve this is the quadradic equation, which is
x = (-B ± sqrt[B^2 - 4C])/(2)
(again, the leading coefficient A is already divided out)
The way Loh does it, however, makes a little more intuitive sense, and the two formulas are a bit simpler.
As I said above, a quadratic equation has two roots. Suppose the number in between the two roots is u.
Then Loh realized that u is just
u = sqrt([B/2]^2 - C)
Very easy, just plug and chug.
After you get u, the roots are just:
x = -(B/2) ± u.
IMHO this is easier. You don't have to do two different calculations into your calculator, which for me already makes it worth the effort to learn a new method.
So in summary, here's how to use the new method to solve quadratic equations:
Step 1: Divide all the terms in the quadratic equation by the leading coefficient (A).
Step 2: Plug B and C into the following formula: u = sqrt([B/2]^2 - C)
Step 3: Plug u into the root formulas, which are -(B/2) ± u.
EDIT- I suppose an example is in order. From a random polynomial generator:
x^2+17x+72 = 0
Step 1 is already done (the leading coefficient is 1).
u = sqrt([17/2]^2 - 72)
u = 0.5
x = - (17/2) ± 0.5
x = -8 and x = -9