**NAME**

Roots_x3Polynomial

**SYNOPSIS**

call Roots_x3Polynomial (real, intent (in) :: c2, real, intent (in) :: c1, real, intent (in) :: c0, integer, intent (out) :: nReal, real, intent (out) :: root (1:3,1:2), logical, optional, intent (in) :: printInfo, integer, optional, intent (in) :: printUnit)

**DESCRIPTION**

Calculates all real + complex roots of the cubic polynomial: x^3 + c2 * x^2 + c1 * x + c0 The first real root (which always exists) is obtained using an optimized Newton-Raphson scheme. The other remaining roots are obtained through composite deflation to a quadratic. The cubic root solver can handle any size of cubic coefficients and there is no danger of overflow due to proper rescaling of the cubic polynomial. The order of the roots is as follows: 1) For real roots, the order is according to their algebraic value on the number scale (largest positive first, largest negative last). 2) Since there can be only one complex conjugate pair root, no order is necessary. 3) All real roots preceede the complex ones.

**ARGUMENTS**

c2 : coefficient of x^2 term c1 : coefficient of x term c0 : independent coefficient nReal : number of different real roots found root (n,1) : real part of n-th root root (n,2) : imaginary part of n-th root printInfo : if given and true, detailed info will be printed about intermediate stages printUnit : the unit ID, where the info will be printed

**NOTES**

Only passing both printInfo AND printUnit will result in printing out the info. Giving only one of them results in no printing action.

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The Flash Center for Computational Science is based at the University of Chicago and is supported by U.S. DOE and NSF.