Quadratics Equations- Solution From The Ancients

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Quadratic equations – a mystery condensed into four terms. Some consider it short and fascinating – like a haiku, while others hate it like a four-letter word!  Love it or hate it, you are not alone- for people have been working on it from as early as 2000 BC. Mathematicians from Ancient Greece, Babylonia, China, Egypt and India had worked on solving quadratic equations, using methods as varied as  completing squares or by using geometry.

Quadratic Equations

Indian Mathematician Brahmagupta’s solution says:

“To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value.”

Sounds like Greek and Latin and spooky?

Don’t worry, translated, it means that,

For a quadratic equation ax2 + bx + c = 0, the solution is

Quadratic Solution Formula

Yes, exactly what your teacher told you.

The ancient Babylonians had quite an interesting method to solve their quadratic equations.

It can be better illustrated through an example.

Consider, x² + 6 x – 7 =0

Bring the constant to RHS

x² + 6x = 7

Factorise LHS

x(x+6) = 7 ——-(1)

Find the average “a” of the factors      [ (x + x+ 6 )/2= x+3 =a]

Now x = a-3 ;  x+6 = a+3;

So (1) becomes (a-3) (a+3) =7

    a2 – 9 = 7

                   a2   = 16

The Babylonians did not use negative numbers, so  a= +4

    x = 4 – 3 = 1

Interesting? Try it out with the next equation you see and tell us if it worked for you.



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