Cubic Equation

Author

Eric W. Weisstein
October 2, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Algebra/CubicEquation.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/CubicEquation.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Equation

Plus@@(Subscript[a,#]x^#&/@Range[0,3])==0//TraditionalForm

Khayyam's conic construction

For x^3 + a x = b, Khayyam intersected a semicircle and a parabola; this example has a = 1, b = 2, and x = 1.

Graphics[{{Directive[LightDarkSwitched[Darker[StandardGray, 0.55], Lighter[StandardGray, 0.55]], AbsoluteThickness[2]], Circle[{-1, 0}, 1, {Pi, 2*Pi}]}, {Directive[RGBColor[0.18, 0.42, 0.68], AbsoluteThickness[2]], Line[Table[{u, -u^2}, {u, -2, 0, 0.02}]]}, {Directive[RGBColor[0.72, 0.24, 0.18], PointSize[0.02]], Point[{-1, -1}]}, Text[Style[x==1, FontFamily -> "Times", 15], {-0.72, -1.14}], Text[Style["semicircle", FontFamily -> "Times", 14], {-1, 0.18}], Text[Style["parabola", FontFamily -> "Times", 14], {-1.65, -2.55}]}, Axes -> True]