2/5/2024 0 Comments Solving a quadratic equation![]() ![]() Let’s talk about a few: Second-degree equationsĪ second-degree equation is a type of equation, and the quadratic equation is considered a second-degree equation. That tiny little “$$2$$” is actually hugely important for placing quadratic equations within the greater context of equation types. Maybe you haven’t heard of a variable being “raised to the second power” before, but you’ve heard of a number or variable being “squared” or “raised to the power of $$2$$.” Lucky for you, they all mean the same thing!Ī variable raised to the second power will look like this: But what does that really mean? And how do you recognize one on the page? Ready to learn quadratic equations? What is a quadratic equation?Ī quadratic equation is an equation in which the variable is raised to the second power. Trust us: giving yourself a little grace will make a world of difference. Allow yourself the time and space to move past that initial shock, and really sit with the information. That said, we know “interesting” can often start out as “confusing.” If that’s where you find yourself, we’re glad you’re here.Īs we start to walk through equations and formulas, it might look overwhelming at first. If you’re just starting to work with quadratic equations, we’re excited for you! That means your algebra adventure is really starting to get interesting (and we do mean “interesting” in a good way!). On Wolfram|Alpha Quadratic Equation Cite this as:įrom MathWorld-A Wolfram Web Resource.Quadratic Equations: Formula, Use, Examples, and Solutions ![]() "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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