Geometric Solution of a Quadratic Equation Using Carlyle's Circle

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This Demonstration shows the geometric solution of the quadratic equation using Carlyle's circle.


The Carlyle circle of the quadratic equation is the circle with diameter , where and . The points where this circle intersects the axis are the roots of the equation. This follows directly from the trigonometric relations and . You can think of the graphics as the solution of the equation .

Drag the black point to change the parameters and .


Contributed by: Izidor Hafner (June 2017)
Open content licensed under CC BY-NC-SA




[1] J. H. Conway and R. K. Guy, The Book of Numbers, New York: Copernicus Books/Springer, 2006 pp. 192–193.

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