Graphical Solution of a Quadratic Equation Using the Arithmetic and Geometric Mean
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.[more]
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.[less]