A new way to make quadratic equations easy
technologyreview.com
A new way to make quadratic equations easy
1–10 of 98 posts
Re: A new way to make quadratic equations easy
#2I don't know that it was ever hard.
Re: A new way to make quadratic equations easy
#3I don't know that it was ever hard.
It is hard for the people that isn't comfortable doing symbolic algebra. I don't see how this method improves it for those.
Re: A new way to make quadratic equations easy
#4I don't know that it was ever hard.
Re: A new way to make quadratic equations easy
#5It would be interesting to have math historian compare this with other derivations of quadratic roots to assess its originality.
My favourite bit of knowledge about quadratic equations is that its roots can always be visualised as the intersection between a simple parabola (x^2) and a straight line (m*x + c).
In fact, the above is why imaginary numbers did not arise from needing to solve quadratic equations. Because in the case of complex roots, the line and the parabola simply do not interesect. So it was originally thought that there was no worthwhile solution anyway. The real 'need' for complex numbers arose from solving cubic equations. [1]
[1] https://www.goodreads.com/book/show/19161684-a-friendly-appr...
Re: A new way to make quadratic equations easy
#6This is bizarre. It’s no less a mathematical trick than completing the square, and it doesn’t seem to be any simpler to use.
The example given is to find the roots of x² - 2x + 4 = 0.
Completing the square gives (x - 1)² + 3 = 0, from which you can immediately see that the roots are 1 ± √3 i. If anything this seems easier than the method of the article.
Am I missing something?
Added: The argument seems to be that young students will find this method easier to understand than completing the square. I have no experience of teaching mathematics to children, so this may be true for all I know. It would be interesting to test this hypothesis experimentally, because I don’t think it’s obviously true.
Re: A new way to make quadratic equations easy
#7I don't know that it was ever hard.
>> to make the quadratic equations easy
They mean: to make the quadratic equation easy to remember.
However, I don't think this will have any impact on the average high school student.
The key is:
>> Loh points out that the two roots, R and S, add up to -B when their average is -B/2.
>> “So we seek two numbers of the form -B/2±z, where z is a single unknown quantity,” he says. We can then multiply these numbers together to get an expression for C.
But you still have to derive the formula and their first example assumes A is fixed.
Re: A new way to make quadratic equations easy
#8Is it just me, or are the images in the article extremely pixelated?
Re: A new way to make quadratic equations easy
#9/r/math discussion: https://www.reddit.com/r/math/comments/dzbmbu/a_new_way_to_s...
Original source: https://www.poshenloh.com/quadratic
Re: A new way to make quadratic equations easy
#10I don't know that it was ever hard.
>> to make the quadratic equations easy They mean: to make the quadratic equation easy to remember. However, I don't think this will have any impact on the average high school student. The key is: >> Loh points out that the two roots, R and S, add up to -B when their average is -B/2. >> “So we seek two numbers of the form -B/2±z, where z is a single unknown quantity,” he says. We can then multiply these numbers toget…
> their first example assumes A is fixed
This is usually how completing the square is taught, in my experience. The leading coefficient is handled later with "just divide everything by a".