# -*- coding: iso-8859-1 -*-
# mk, 26.8.08

from math import sqrt

def quadglei(a,b,c):
    """ Rückgabe: [Anzahl der Lösungen, Lösungen], [3]=unendl.

    >>> quadglei(0,0,0)
    [3]
    >>> quadglei(0,0,1)
    [0]
    >>> quadglei(0,1,2)
    [1, -2.0]
    >>> quadglei(7,7,-84)
    [2, -4.0, 3.0]
    >>> quadglei(1,2,-3)
    [2, -3.0, 1.0]
    >>> quadglei(10,1,0.025)
    [1, -0.050000000000000003]
    >>> (abs(quadglei(10,1,0.025)[1]--0.05)<1e-10)
    True
    >>> quadglei(10,1,1)
    [0]
    """
    if a==0:
        if b==0:
            if c==0:
                return [3]
            else:
                return [0]
        else:
            x = float(-c)/b
            return [1,x]
    else:
        d = b*b-4*a*c
        if d>0:
            wd = sqrt(d)
            x1 = (-b-wd)/float(2*a)
            x2 = (-b+wd)/float(2*a)
            return [2,x1,x2]
        else:
            if d==0:
                x = -b/float(2*a)
                return [1,x]
            else:
                return [0]

if __name__ == "__main__":
    import doctest
    doctest.testmod(verbose=True)