Graphical Solution of a Quadratic Equation Using a Result from Optics

This Demonstration shows a graphical solution of the quadratic equation . If and are the roots of the equation, then and . So , where . From optics, if a convex lens with focal length is located at the point , then . We must find the position of so that . The harmonic mean of and is . Since , can be constructed by Euclidean geometry.

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