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Graphical Solution of a Quadratic Equation Using the Arithmetic and Geometric Mean

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This Demonstration shows a graphical solution of the quadratic equation . If and are the solutions of the equation, then and . So is the arithmetic mean of and , and is the geometric mean.

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Construct a triangle with vertical leg and hypotenuse . Let and be the intersection of the extension of the horizontal leg and the circle with center and radius .

Then and are the solutions of the equation.

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Contributed by: Izidor Hafner and Marko Razpet (October 2018)
Open content licensed under CC BY-NC-SA

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