Farebrother, "Simplified Samuelson conditions for cubic and

quartic equations," The Manchester School, vol.

Like all

quartic equations, solving this in a closed form is possible but difficult to do robustly [10].

The biggest problem of the discrete analysis is the huge amount of cubic and quartic equations that should be calculated.

An exact analysis in the final balance is complicated because there is a need to calculate numerous cubic and quartic equations to find [u.sub.i+1] - [u.sub.i] and there is no usable analytical solution.

As a result, all cubic and quartic equations are transformed to quadratic equations.

Mathematics of the first year in high school includes: Sets, Real and Complex numbers, Discriminant, Cubic and

Quartic Equations, Quadratic Inequality, Means, Distribution and Standard Deviation, Equation of Lines, Equation of Circles, Parallel Transformation, Composite Functions, Inverse Functions, Maxima and Minima of Quadratic Functions, Rational Functions, Radians, Trigonometric Functions, Laws of Sine and Cosine, Area of Triangles.

Linear, quadratic, cubic, and

quartic equations were tested to determine which gave the best fit to the data.

Other important additions to the library include routines for finding the roots of real and complex cubic and

quartic equations, and for solving Black-Scholes equations.

The elegant radical solutions of cubic and quartic equations by Nicolo Tartaglia (c, 1543) and L.

An interesting problem started Omar Khayyam on employing conic sections in solving cubic and quartic equations. It is desired to divide the one fourth AB of the circle ABCD by a point R into two parts such that, if RH is drawn perpendicular to the diameter BD, (11) is obtained