Graphical Solution of a Quadratic Equation Using a Result from Optics
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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.
Contributed by: Izidor Hafner (October 2018)
Open content licensed under CC BY-NC-SA
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