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The first method, the quadratic formula, works regardless of what format the quadratic equation comes in. There are two main ways of solving a quadratic formula. (a = 9, b = 0, c = -81 since we could subtract 81 from both sides) Root - A solution to an equation such as a quadratic equation such that f(x) = 0.įor example, for the quadratic equation x 2 + x - 12 = 0, x = 3 and x = -4 are both roots since f(3) = 3 2 + 3 - 12 = 0 and f(-4) = (-4) 2 - 4 - 12 = 0Īlthough all quadratic equations by definition fit the form ax 2 + bx + c = 0, the most common simple format for a quadratic equation is as follows:.In this case, the equation x 2 - x - 2 = 0 can be broken apart into two factors such that when these two separate terms (i.e., factors) are multiplied together, the result is the original equation.
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Factoring - The process of breaking apart of an equation into factors (or separate terms) such that when the separate terms are multiplied together, they produce the original equation.įor example, x 2 - x - 2 = (x+1)(x-2).Quadratic Equation - An equation that can be written in the form ax 2 + bx + c = 0.įor example, 2x 2 + 3x + 2 = 0 is a quadratic equation while 3x + 2 is not a quadratic equation.Solving Quadratic Equations: The Quadratic FormulaĪ quadratic equation takes the form ax 2 + bx + c = 0.Examples of Complex or Untraditional Quadratic Equations.