Unit 7 Who Created the Quadratic Formula?

x = [-b ± √(b² - 4ac)]/2a

Through the use of non-linear equations, complex mathematical problems such as the trajectories of weapons fire can be solved...  but who created the quadratic formula that is used to solve the polynomial expressions that describe these types of phenomena. Man has been using complex mathematical principles for 1000s of years to solve its problems. The principles of mathematics were long applied primarily to pragmatic problems rather that being studied for their theoretical interest. From the years of about 2000 BC up until approximately 300 BC, construction required solutions of this type.

Mathematical Problems

Many problems related to calculating the area of buildings required to store items. There is evidence that engineers and construction workers in China, Egypt and Babylonia faced the same problems on a regular basis. They solved their problems by using lookup tables as a reference tool to reach the answers that they required for their building projects. In fact, most mathematicians up until the time of Euclid  in 300 BC used either look-up tables to find the values that met their needs or they used a method called completing the square.

The Chinese were a bit quicker in calculating some of their own tables due to the rapid calculations that they could accomplish with the abacus. All of these lookup tables had the drawback of allowing error to creep into the tables in the copying process. All of these lookup tables would become obsolete in a few thousand years in the future by the quadratic formula. Little did the early engineers know that  the men who created the quadratic formula would come from the parts of the world in which they lived.

Who Created the Quadratic Formula?

While most mathematicians before him had used lookup tables instead of trying to create a formula, Euclid was able to put forward a general equation that would calculate the square root of an area. This formula would give the length of sides required to provide the requested area. An extension of this general formula would include calculating the area and dimensions of a rectangular room or space.

While Euclid began the process, most of the further work done on the general form of the quadratic formula occurred between 700 AD and about 1100 AD in both India and in Islamic countries.

The precursor to what is known today as the quadratic formula, was derived by an Islamic mathematician named Mohammed bin Musa Al-Khwarismi. He derived the formula at about the same time as an Indian mathematician named Baskhara did.

Looking at how the formula was developed suggests that, to answer who created the quadratic formula you would have to cite both Baskhara from India and Al-Khwarismi from an area near Baghdad.

Both of these men realized that there were two answers to the quadratic formula, called "roots," but neither of them would allow for a negative root. They did allow both rational and irrational numbers to be used, however.