![]() It is derived from using the previous method (complete the square) on a general quadratic in standard form: ax 2 + bx + c = 0. Quadratic Formula – this method always works.We also use the method of completing the square to put certain circle equations into the proper form. The quadratic formula is a shortcut for this method. Complete the Square – this method is a long one, but it works.However, some quadratics are difficult to factor, and the quadratic formula would be more helpful in those cases. Factoring– this method is helpful in some cases to avoid the work of graphing, completing the square, or using the quadratic formula.Also, the graph will not intersect the x-axis if the solutions are complex (in the case of a negative discriminant). The only drawback is that it can be difficult to find exact values of x. If you graph the quadratic function f(x) = ax 2 + bx + c, you can find out where it intersects the x-axis. Graphing – this is a good visual method if you have the vertex form of a parabola or if you have a parabola-like curve from a data set.Here are four methods you can use to solve a quadratic equation: We’ll also take a closer look at how these methods are connected to each other. In this article, we’ll talk about the four methods you can use to solve a quadratic equation and give some examples for each one. However, it might be easier to factor in some cases to avoid radicals and fractions in the quadratic formula. Of course, the quadratic formula will work for any quadratic equation you choose. If factoring is hard, the quadratic formula (a shortcut for completing the square) helps. ![]() Graphing gives a good visual, but it is hard to find values of x from a graph with no equation. So, how do you solve quadratic equations? You can solve quadratic equations by graphing, factoring, completing the square, & the quadratic formula. Luckily, there are several ways to do it. On Wolfram|Alpha Quadratic Equation Cite this as:įrom MathWorld-A Wolfram Web Resource.Quadratic equations come up often in mathematics and physics, and it is vital to know how to solve them. "The Quadratic Function and Its Reciprocal." Ch. 16 in AnĪtlas of Functions. Cambridge, England:Ĭambridge University Press, pp. 178-180, 1992. Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. "Quadratic and Cubic Equations." §5.6 in Numerical Oxford,Įngland: Oxford University Press, pp. 91-92, 1996. ![]() Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. "Quadratic Equations."Īnd Polynomial Inequalities. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. Viète was among the first to replace geometric methods of solution with analytic ones, although he apparently did not grasp the idea of a general quadratic equation (Smith 1953, pp. 449-450).Īn alternate form of the quadratic equation is given by dividing (◇) through by : The Persian mathematiciansĪl-Khwārizmī (ca. 1025) gave the positive root of the quadratic formula, as statedīy Bhāskara (ca. 850) had substantially the modern rule for the positive root of a quadratic. Of the quadratic equations with both solutions (Smith 1951, p. 159 Smithġ953, p. 444), while Brahmagupta (ca. (475 or 476-550) gave a rule for the sum of a geometric series that shows knowledge The method of solution (Smith 1953, p. 444). Solutions of the equation, but even should this be the case, there is no record of ![]() ![]() It is possible that certain altar constructions dating from ca. 210-290) solved the quadratic equation, but giving only one root, even whenīoth roots were positive (Smith 1951, p. 134).Ī number of Indian mathematicians gave rules equivalent to the quadratic formula. In his work Arithmetica, the Greek mathematician Diophantus The Greeks were able to solve the quadratic equation by geometric methods, and Euclid's (ca. ![]()
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