The Indian mathematician Brahmagupta (597–668 AD) was first to clearly describe the quadratic formula, although prior civilizations had investigated quadratic equations, understood them fairly well, and developed methods for solving them.
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The Indian mathematician Brahmagupta, in Brahma-Sphuta-Siddhanta (written in A.D. 628), discussed the use of negative numbers to produce the general form quadratic formula that remains in use today.
The solutions to this equation are called the roots of the quadratic polynomial, and may be found through factorization, completing the square, graphing, Newton's method, or through the use of the quadratic formula.
Linear polynomials are easy to solve, but using the quadratic formula to solve quadratic (second degree) equations may require some care to ensure numerical stability.