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Question about this guy's new quadratic solving method

  • 10-12-2019 10:58pm
    #1
    Registered Users Posts: 4,540 ✭✭✭


    Just trying to visualise his method graphically and want to double check.

    https://www.popularmechanics.com/science/math/amp30152083/solve-quadratic-equations/

    So at 1:46 when he says the 2 numbers must be the same distance away from their average. Does he mean the "average" is the X value which is half way between the 2 roots?

    Anyone any other solving quadratic method besides the -b , completing the square or guessing by add and multiply?


Comments

  • Registered Users Posts: 5,141 ✭✭✭Yakuza


    That. Was. Stunning(ly beautiful in its simplicity).
    Mind. Blown.

    Yes, as best as I can make out the average he refers to is the average of the two roots. Chosing it in the form he does makes the product (x+u)(x-u) = x²-u² which he can then solve easily. I am stunned at how simple he's made it.


  • Registered Users Posts: 1,768 ✭✭✭timsey tiger


    I really like this method. Thanks for sharing it.

    Another method is completing the squares, which is typically used in deriving the -b formula.

    This method is kind of the same as completing the squares, but I think that it seems much simpler to explain.


  • Registered Users Posts: 3,522 ✭✭✭zv2


    This is amazing. I'm looking at it in terms of modular arithmetic:

    ax = 1 (mod m)

    (a + x)/2 = u

    u^2 - v^2 = 1 (mod m)

    “Those who can make you believe absurdities can make you commit atrocities.” — Voltaire



  • Registered Users Posts: 8,219 ✭✭✭Gaoth Laidir


    Where did he get the 4 to begin with? Why 4?


  • Moderators, Science, Health & Environment Moderators Posts: 1,846 Mod ✭✭✭✭Michael Collins


    Because if you have two numbers that sum to 8 i.e.

    y + z = 8

    their average must be

    (y + z)/2 = 4.

    The average is useful, because the average of two numbers is always exactly midway between the two.

    In this case:

    y............4............z
    <---u---> <---u--->

    So, in this example, y is 4 - u and z is 4 + u.
    Proof that average of two numbers lies midway between the two numbers:
    
    Distance of y from average:
    
    (y + z)/2 - y = (z - y)/2
    
    Distance of z from average:
    
    z - (y + z)/2 = (z - y)/2
    
    i.e. both the same.
    
    


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