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Quartic equation

A quartic equation is the result of setting a quartic function to zero, an example quartic equation is the equation


the general form is

a4x4+a3x³+a2x²+a1x+a0=0, and a4≠0.

A quartic equation always has 4 solutions (or roots).They may be complex or there may be duplicate solutions.

It is the highest degree of polynomial equation for which exact values of the roots can be found, by taking nth roots, and use of the normal algebraic operators.

If a0=0, then one of the roots is x=0, and the other roots can be found, by dividing by x, and solving the resulting cubic equation, a4x³+a3x²+a2x+a1=0.

Otherwise, divide the equation by a4, to get an equation of the form


Substitute x=t-a/4, to get an equation of the form

Then find the roots somehow. (To be written.)

See also