Say I have a monic polynomial,(adsbygoogle = window.adsbygoogle || []).push({});

x^3 + ax^2 + bx + c

with a=-2.372282, b=1.862273, c=-0.483023

The discriminant is given by

a^2 b^2 - 4 b^3 - 4 a^3 c - 27 c^2 + 18 ab c

which is < 0, indicating 1 real root and 2 complex conjugates.

A method for solving a general cubic using the Chebyshev root is explained here,

http://www.statemaster.com/encyclopedia/Cubic-equation

but (a^3 - 3b) is negative, which means that "t" will be imaginary. But t is then used in the Chebyshev cubic root, which is only defined for real numbers [-2, inf].

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# Chebyshev cubic roots

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