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The solutions of the quadratic equation ax 2 + bx + c = 0 correspond to the roots of the function f(x) = ax 2 + bx + c, since they are the values of x for which f(x) = 0. If a , b , and c are real numbers and the domain of f is the set of real numbers, then the roots of f are exactly the x - coordinates of the points where the graph touches the ...
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations.
A similar but more complicated method works for cubic equations, which have three resolvents and a quadratic equation (the "resolving polynomial") relating and , which one can solve by the quadratic equation, and similarly for a quartic equation (degree 4), whose resolving polynomial is a cubic, which can in turn be solved. [14]
Wolfram Alpha: Wolfram Research: 2009 2013: Pro version: $4.99 / month, Pro version for students: $2.99 / month, ioRegular version: free Proprietary: Online computer algebra system with step-by step solutions. Xcas/Giac: Bernard Parisse 2000 2000 1.9.0-99: May 2024: Free GPL: General CAS, also adapted for the HP Prime. Compatible modes for ...
WolframAlpha gathers data from academic and commercial websites such as the CIA's The World Factbook, the United States Geological Survey, a Cornell University Library publication called All About Birds, Chambers Biographical Dictionary, Dow Jones, the Catalogue of Life, [1] CrunchBase, [10] Best Buy, [11] and the FAA to answer queries.
Given a transformation between input and output values, described by a mathematical function, optimization deals with generating and selecting the best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the output of the function and recording the best output values found during the process.
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MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constrained, conic and convex nonlinear mathematical optimization problems. The applicability of the solver varies widely and is commonly used for solving problems in areas such as engineering, finance and computer ...