## Applet showing Lill's method applied to quadratic equations

Applet figure showing the right-angle paths that represent a quadratic equation with real solutions

The horizontal blue line is the x-axis where the point **O** represents x = 0, and distances are measured in units of **a**, the fixed distance between points **O** and **SP** (starting point). The positive coefficients, **b** and **c** can be adjusted by moving the points **B** and **C**, respectively. The point **x** is at the end of one purple line connected to the starting point **SP**, and can slide along the x-axis until the Point **P** coincides with the point **C**. This will happen at the two locations, where **x** falls on the point where the blue circle intersects the x-axis. The solution values of **x** are then given by the distance between points **O** and **x**. The value of **x** is positive when the point **x** is to the right of the point **O**, and negative otherwise. If the blue circle does not intersect the x-axis, the point **x** cannot rest on any point along the x-axis where the points **P** and **C** can coincide, therefore the roots are complex.
If the mouse cursor is clicked on the applet and then the space bar is pressed, the applet will reset to its original position. The applet can be enlarged by clicking on the applet, pressing the return key, and dragging the lower right corner of the applet to any desired size.

### References