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Quadratic equation

  1. Feb 18, 2008 #1
    who came up with the Quadratic equation and what is the proof behind it?
     
  2. jcsd
  3. Feb 18, 2008 #2
  4. Feb 19, 2008 #3

    Gib Z

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    Homework Helper

    It's just completing the square, but used on the general form of the quadratic equation. I can't remember who first proved it though :( Some Arabic mathematician i think.
     
  5. Feb 19, 2008 #4
    Take ax^2+bx+c=0 complete the square and you'll obtain the quadratic equation.
     
  6. Feb 19, 2008 #5
    The latest edition of the Mathematics Teacher, published by the NCTM has a different way to derive the quadratic formula than completing the square.

    It is actually kind of elegant as well.
     
  7. Feb 20, 2008 #6
    what is it?
     
  8. Feb 20, 2008 #7
    Yeah I'm curious too
     
  9. Feb 20, 2008 #8
    Dang, I knew I should have brought my copy home. I will look it up and post later.
    -------
    Ok, looked it up. It is complex, so I will have to short cut it. The full citation, if interested is:
    Piccioto, Henry. (February 2008). A new path to the quadratic formula. Mathematics Teacher 101:6, 473-478.

    If there are roots p and q, then the function can be written in factored form
    y=a(x-p)(x-q) = x^2 - a(p+q)x + apq

    It follows that the product of the roots is c/a, since c=apq and the sum of the roots is -b/a, since b= -a(p+q).

    From here, he uses that information to find (h,v), the co-ordinates of the vertex. The average of the roots, h, is -b/2a. This is then substituted into the formula to get v, and the resultant is

    v= (-b^2 +4ac)/4a

    Notice that this is the discriminant divided by 4a!

    Finally, the author notes that the x intercept is on either side of the vertex by the same amount, d, so x = -b/2a +- d, and if we move the parabola so that the vertex is at the origin, it's equation simply becomes y=ax^2.

    With this new translated parabola, we can then do a little algebra (which is explained in the article, 2 steps) to get x = the negative boy couldn't decide on whether to attend a radical party or be square, so he missed out on 4 awesome chicks and the party was all over by 2 am.

    It is a very visual method, instead of the normal completing the square method.

    There is no way I did it justice in my re-telling.
     
    Last edited: Feb 20, 2008
  10. Feb 27, 2008 #9
    what is ^?
     
  11. Feb 27, 2008 #10

    uart

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    Science Advisor

    Exponentiation. It means "raised to the power of"
     
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