Two Types of Quadratic Formula
Posted by chanheeh on December 2, 2008
When I was a high school student in Korea, I learned two types of quadratic formula.
If the quadratic equation is in the form of 
.
As you know, the first quadratic formula is the famous 
.
We learned one more thing. The other one is used only if b is a even number.
If we let b be 2d in the quadratic equation, it will be 
, right?
Then, the new quadratic formula becomes 
.
You already figured out how I got the second one!!
If we substitute 2d into b in the original quadratic formula,
we could get 
,
which is 
and we can just reduce them.
And finally got the new quadratic formula 
,
when the quadratic equation is 
.
Do you know why we used two types of quadratic formula in Korea? We had to solve all the math problems mentally without any calculator in a short time. Believe or not, the second quadratic formula sometimes helped me a lot to save time!
You can try it now.
Solve 
using the second type of quadratic formula
(Hint: in this case, d becomes 12/2, which is 6)
Chanhee's Math Blog 
Young said
The second one would be really helpful for saving time, especially when the coefficient of x is a kind of big number, but only if I don’t have a calculator in my hand!!
Nadya Fermega said
Wonderful, I apply soon in my homework
Denaya Lesa said
Maybe the utility of quadratic formula becomes a reason why for D=d/dt the damped oscillation (D^2)x + rDx + c*x = 0 has been commonly written as (D^2)x + 2bDx + c*x = 0 .