How to use this applet:
The applet starts up in "Graph" mode. This will display a cubic equation with coefficients a, b, c and d. Using the scrollbars you can adjust these coefficients. This way you can easily see that there is a minimum of 1 and a maximum of three roots for a cubic equation. (Note that if a = 0, the equation is not cubic!)
In "calculator" mode (press the button "Calculator mode" to switch), the applet shows to to find the roots for an equation when one complex root is given and the coefficients are all real. Note that you need to enter at least a second order (ie., quadratic) equation.
Notes on the maths used in the applet:
The conjugate roots theorem says that if z is a solution to a quadratic equation, and all the coefficients of the equation are real, then the conjugate of z is the other root for the equation.
If the equation is cubic, two roots can be found this way. The third root should be determined using the quadratic factor. The applet explains this in detail.
