**NAME**

Roots_x2Polynomial

**SYNOPSIS**

call Roots_x2Polynomial (real, intent (in) :: q1, real, intent (in) :: q0, integer, intent (out) :: nReal, real, intent (out) :: root (1:2,1:2))

**DESCRIPTION**

Calculates all real + complex roots of the quadratic polynomial: x^2 + q1 * x + q0 The code checks internally, if rescaling of the coefficients is needed to avoid overflow. 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.

**ARGUMENTS**

q1 : coefficient of x term q0 : independent coefficient nReal : number of real roots found root (n,1) : real part of n-th root root (n,2) : imaginary part of n-th root

**NOTES**

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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.