Civil Engineering Reference
In-Depth Information
Closed-form formula for the roots of cubic and quartic equations
This appendix reproduces results on the solution of cubic and quartic equations
[Ric66].
A.1 CUBIC EQUATIONS
A general cubic equation is given by
Setting
this becomes
where
and
Further substituting
this
reduces to
This is a quadratic in
which may be solved to yield six roots for
namely‚
and
where
