Note that it is also possible to solve cubic equations geometrically. On Wolfram|Alpha Quadratic Equation Cite this as:įrom MathWorld-A Wolfram Web Resource. You can solve quadratic equations directly using straight edge and compass constructions. "The Quadratic Function and ItsĪtlas of Functions. Cambridge, England:Ĭambridge University Press, pp. 178-180, 1992. Quadratic equations are solved using one of three main strategies: factoring, completing the square and the quadratic formula. In this formula, a, b, and c are number they are the numerical coefficient of the quadratic. Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Answer: The general quadratic equation formula is ax2 + bx + c. Quadratic Formula: x b±b2 4ac 2a x b ± b 2 4 a c 2 a. For equations with real solutions, you can use the graphing tool to visualize the solutions. ![]() The Quadratic Formula Calculator finds solutions to quadratic equations with real coefficients. "Quadratic and Cubic Equations." §5.6 in Numerical Step 1: Enter the equation you want to solve using the quadratic formula. 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. These also arise naturally when solving real-world problems. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. The general form of a quadratic equation is ax2+bx+c0, where a,b,c are given numbers with a0. 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 : When the Discriminant ( b24ac) is: positive, there are 2 real solutions. The Persian mathematiciansĪl-Khwārizmī (ca. Quadratic Equation in Standard Form: ax 2 + bx + c 0. 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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