Consider the equation
[math] \;\;\; f(x) = x³+ c_2x² + c_1 x + c_0[/math]
How shall we go about its solution? First of all, [i]can we make the problem go away?[/i] For example, suppose we shift f(x) to the left or right until it has a zero at x=0:
[math]\;\;\; g(x) = x³+ d_2x² + d_1 x,[/math]
Divide out x, and the last two roots can be found using the quadratic equation.
If I write g(x) = f(x-t), is it possible to solve for the mystery offset t and the new coefficients?
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Roots of the Cubic Equation
Solution 1 (Iterative): [url]http://tube.geogebra.org/material/show/id/143036[/url]
Solution 2 (Algebraic): [url]http://tube.geogebra.org/material/show/id/143424[/url]
