import math


def _realroots_quadratic(a1, a0):
    """gives the real roots of x**2 + a1 * x + a0 = 0"""
    D = a1*a1 - 4*a0
    if D < 0:
        return []
    SD = math.sqrt(D)
    return [0.5 * (-a1 + SD), 0.5 * (-a1 - SD)]