The linear equation first appeared in Diophantine's works, but he didn't put it forward first. Tracing back to the source, the invention right of quadratic equation belongs to mathematicians in ancient China and Babylonia. However, in 2000 BC, Babylonian arithmetic had developed into a highly developed algebra described in words. They can not only substitute the equivalent equation into the general formula, but also solve the quadratic equation by matching method. In the 20th century BC, China also mastered quadratic equations and often transformed them into linear equations. In "Nine Chapters Arithmetic", the oldest quadratic equation is: "Now there is a square pool one foot, longer than the center, one foot out of the water, leading to the shore and suitable for the shore. Ask the geometry of the water depth. " Indian mathematician Bashgaro mentioned a "lotus problem" in his works, which is completely similar to the solution of "leading to the other side" in Nine Chapters of Arithmetic. It is described as follows: "The waves in the lake are quiet and the lotus is new, and the five-inch Tingting is smiling. I don't care if the wind blows through the grave, but I can't bear to see the colors without ripples. Fishermen look for roots after autumn, and the roots are two feet away from the flowers. I would like to ask the students of Qun Yingxian how deep the water was. "

Actually, we can set the water depth to x feet. After the lotus was blown down by the wind, the flowers floated on the water. Then, the stem length should be x+0. According to the Pythagorean theorem equation, tilt 5 feet in the water.

x ^ 2+2 ^ 2 =(x+0.5)2

X=3.75 feet

Although the solutions of "Lotus Problem" and "Painting ashore" are the same, both belong to quadratic equation problems, but they are at least later than China's "Painting ashore" 1000 years. According to available data, the quadratic equation of India was introduced into India from China by Buddhists in the 3rd-9th century.

The general solution of quadratic agenda in Nine Chapters Arithmetic is earlier than that in Europe 1000. In Liu Zheng's hands, he created the method of fractional roots by using the principle of solving quadratic equations.