Editing Cubic equation (section)

==Applications==
Cubic equations arise in various other contexts.

===In mathematics===
* [[Angle trisection]] and [[doubling the cube]] are two ancient problems of [[geometry]] that have been proved to not be solvable by [[straightedge and compass construction]], because they are equivalent to solving a cubic equation.
* [[Marden's theorem]] states that the [[focus (geometry)|foci]] of the [[Steiner inellipse]] of any triangle can be found by using the cubic function whose roots are the coordinates in the [[complex plane]] of the triangle's three vertices. The roots of the [[first derivative]] of this cubic are the complex coordinates of those foci.
* The [[area]] of a regular [[heptagon]] can be expressed in terms of the roots of a cubic. Further, the ratios of the long diagonal to the side, the side to the short diagonal, and the negative of the short diagonal to the long diagonal all satisfy a particular cubic equation. In addition, the ratio of the [[inradius]] to the [[circumradius]] of a [[heptagonal triangle]] is one of the solutions of a cubic equation. The values of trigonometric functions of angles related to <math>2\pi/7</math> satisfy cubic equations.
* Given the cosine (or other trigonometric function) of an arbitrary angle, the cosine of [[angle trisection|one-third of that angle]] is one of the roots of a cubic.
* The solution of the general [[quartic equation]] relies on the solution of its [[resolvent cubic]].
* The [[eigenvalue]]s of a 3×3 [[matrix (mathematics)|matrix]] are the roots of a cubic polynomial which is the [[characteristic polynomial]] of the matrix.
* The [[characteristic equation (calculus)|characteristic equation]] of a third-order constant coefficients or [[Cauchy–Euler equation|Cauchy–Euler]] (equidimensional variable coefficients) [[linear differential equation]] or [[difference equation]] is a cubic equation.
* Intersection points of cubic [[Bézier curve]] and straight line can be computed using direct cubic equation representing Bézier curve.
* [[Critical point (mathematics)|Critical points]] of a [[quartic function]] are found by solving a cubic equation (the derivative set equal to zero).
* [[Inflection point]]s of a [[quintic function]] are the solution of a cubic equation (the second derivative set equal to zero).

===In other sciences===
* In [[analytical chemistry]], the [[Charlot equation]], which can be used to find the pH of [[buffer solution]]s, can be solved using a cubic equation.
* In [[thermodynamics]], [[equation of state#Cubic equations of state|equations of state]] (which relate pressure, volume, and temperature of a substances), e.g. the [[Cubic_equations_of_state#Van_der_Waals_equation_of_state|Van der Waals equation of state]], are cubic in the volume.
* [[kinematics|Kinematic equations]] involving linear [[jerk (physics)|rates of acceleration]] are cubic.
* The speed of seismic Rayleigh waves is a solution of the [[Rayleigh wave#Rayleigh wave dispersion|Rayleigh wave]] cubic equation.
* The steady state speed of a vehicle moving on a slope with air friction for a given input power is solved by a depressed cubic equation.
* [[Kepler%27s_laws_of_planetary_motion#Third_law|Kepler's third law]] of planetary motion is cubic in the semi-major axis.