The graph of any quadratic function has the same general shape, which is called a parabola. The function f( x) = ax 2 + bx + c is a quadratic function. 101) and more properly for a quartic equation having no odd powers, i.e., z4+a2z2+a00. 34), but perhaps more commonly (e.g., Hazewinkel 1988 Gellert et al. Its x-intercepts are rotated 90° around their mid-point, and the Cartesian plane is interpreted as the complex plane ( green). The term 'biquadratic equation' is sometimes used to as a synonym for quartic equation (Beyer 1987b, p. Visualisation of the complex roots of y = ax 2 + bx + c: the parabola is rotated 180° about its vertex ( orange). Thus the roots are distinct if and only if the discriminant is non-zero, and the roots are real if and only if the discriminant is non-negative. In these expressions i is the imaginary unit. Which are complex conjugates of each other. On Wolfram|Alpha Quadratic Equation Cite this as:įrom MathWorld-A Wolfram Web Resource.A x 2 + b x + c = 0, ![]() "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 : To find out the roots (zeros) of a second degree function, start by placing that. The Persian mathematiciansĪl-Khwārizmī (ca. Using the quadratic formula: number of solutions. 1025) gave the positive root of the quadratic formula, as statedīy Bhāskara (ca. Worked example: quadratic formula (negative coefficients) Quadratic formula. 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. Just enter the factors a, b and c below, and press 'Get Results' Your Equation: Solution 1: Solution 2: Discriminant: Note: Is it Quadratic Only if it can be put in the form ax2 + bx + c 0, and a is not zero. In his work Arithmetica, the Greek mathematician Diophantus Quadratic Equation Solver If you have an equation of the form 'ax2 + bx + c 0', we can solve it for you. ![]() The Greeks were able to solve the quadratic equation by geometric methods, and Euclid's (ca.
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