What Is The Origin Of The Formula For The Solution Of Quadratic Equations?

The formula for solving quadratic equations, also known as the quadratic formula, has its origins in ancient Greece and the work of mathematicians such as Pythagoras and Euclid. However, the specific form of the quadratic formula that is used today was first derived by the Persian mathematician and astronomer, Omar Khayyam, in the 11th century.

The quadratic formula is used to solve equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. The formula expresses the solutions for x in terms of a, b, and c, and is as follows:

x = (-b ± √(b^2 - 4ac)) / 2a

The formula is based on the idea of completing the square, which involves adding and subtracting the square of half of the coefficient of x, in order to make the expression on one side of the equation a perfect square. Once the equation is in this form, it can be factored and the solutions for x can be determined.

This technique was known and used by the Greek and Indian mathematicians, but Omar Khayyam was the first one to put it in a general form for any quadratic equation.