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Sign up using Facebook. The history of the quadratic formula can be traced all the way back to the ancient Egyptians. The theory is that the Egyptians knew how to calculate the area of different shapes, but not how to calculate the length of the sides of a given shape, e. To solve the practical problem, by around BC, Egyptian mathematicians had created a table for the area and side length of different shapes.
This table could be used, for example, to determine the size of a hayloft needed to store a certain amount of hay. While this method worked fine, it was not a general solution. The next approach may have come from the Babylonians, who had an advantage over the Egyptians in that their number system was more like the one we use today although it was hexagesimal, or base This made addition and multiplication easier. It is thought that b y around BC, the Babylonians had developed the method of completing the square to solve generic problems involving areas.
A similar method also appears in Chinese documents at around the same time. The completing square method allowed the Babylonians and Chinese to cross-check the area values that they calculated for different purposes. The first attempts to find a more general formula for solving quadratic equations may have been made by Greek philosophers Pythagoras c.
Pythagoras observed that the value of a square root value is not always an integer. However, he refused to allow for proportions that were not rational. Euclid, in his mathematical treatise Elements, proposed that irrational square roots are also possible.
However, because the ancient Greeks did not use the same number system that we now use, it was not possible to calculate the square root by hand, which is what architects and engineers really needed.
Indian mathematics used the decimal system. It also had one other advantage over the system used by the ancient Egyptians and Greeks — the zero. Zero allowed mathematicians to not only theorize about irrational numbers but to use them in equations.
Brahmagupta recognized that there are two roots in the solution to a quadratic equation and described the quadratic formula as, "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.
This was also one of the first works to describe concrete ways of using zero. He solved the quadratic equation using algebraic expressions although he rejected negative solutions and is often credited as the father of algebra. His work made its way to Europe by around AD, where it was translated into Latin.
By , Italian scientist Gerolamo Cardano had compiled works related to the quadratic equations, including both Al-Khwarizmi's solution and Euclidean geometry. In his works, he allows for the existence of roots of negative numbers.
Flemish engineer and physicist Simon Stevin gave the general solution of the quadratic equation for all cases in his book Arithmetic in the year Descartes's work included the quadratic formula in the form we know today. Quadratic equation came into existence because of the simple need to conveniently find the area of squared and rectangular bodies, but from the days of its origin, this popular maths equation has now come a long way to prove its significance in the real world.
The quadratic formula is among the fundamental principles of modern-day mathematics. Every future engineer, scientist, or mathematician is destined to face the quadratic equation in one or the other form.
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