Solving the univariate cubic equation is a famous, complex and interesting problem in the history of world mathematics. The introduction of the concept of imaginary number and the establishment of complex number theory originated from the solution of cubic equation problems. 1545, an Italian scholar Caldan (cardano,1501-1576, translated into cardano) published a formula for finding the root of cubic equation x 3+px+q = 0. Caldan was the first mathematician to write negative numbers in quadratic roots, and thus introduced negative numbers.
To solve a cubic equation with roots, although there is a famous Caldan formula and the corresponding discrimination method, it is more complicated and lacks intuition to solve the problem with Caldan formula.
Cubic equation is widely used, such as meteorology, power engineering, electrical engineering, water conservancy engineering, architectural engineering, mechanical engineering, power engineering, chemical engineering, biological engineering, aerospace engineering, software engineering, military engineering, national defense technology, electronic technology, mathematics research, mathematics teaching, mathematics culture, mathematics thinking quality training, mathematics history education, mathematics aesthetics education and so on. , and these fields all use solution III.
From 65438 to 0969, after learning and mastering the knowledge of understanding the quadratic equation of one yuan in junior high school, Shenjin Fan became interested in solving the cubic equation of one yuan.
From 65438 to 0978, after Shenjin Fan became a middle school math teacher, he began to think about how to work out a more practical formula for finding roots than Cardin's formula.
1988, after in-depth research and exploration, Shenjin Fan deduced a set of discriminant A = B 2-3ac with the method of mathematical beauty. B = 9adC = c 2-3bd BC and the total discriminant δ = b 2-4ac constitute the simplest form, which is easy to remember and efficient in solving problems. It is more practical than the formula of finding the root of a cubic equation by Kardan, and a simple, intuitive and practical new discriminant, the Jinsheng discriminant method, is established.
Especially: when δ = b 2-4ac = 0, the formula ③: x (1) =-b/a+k; X = x =-k/2, where K=B/A, (A≠0). Concise and easy to remember, there is no square root (the square root of Kadan formula still exists at this time). Jinsheng Formula ③ Manual problem solving is efficient.
Jinsheng formula ③ is called super simple formula.
Jin Sheng's formula for solving problems, "A new root formula and a new judgment method for a cubic equation with one variable", was published in Journal of Hainan Normal University (Natural Science Edition), No.2 1989.
When experts and scholars encounter practical problems in solving cubic equations in scientific research and engineering technology, Jinsheng formula is widely used.