众所周知,三次方程总有三个复根.任给一个实系数一元三次方程ax~3+bx~2+cx+d=0(a≠0),当常数项d在(-∞,+∞)上变化时,该方程的三个复根在复平面上表示的点将运动形成曲线轨迹.那么这个轨迹是什么呢?本文对这个问题进行探讨,并得到了许多美妙的结论.命题1上述轨迹为双曲线(极限 It is well-known that there are always three complex roots in a cubic equation, given a real cubic univariate equation ax 3 + bx 2 + cx + d = 0 (a ≠ 0). When the constant d is on (-∞, + ∞) When changing, the points represented by the complex roots of the three complex roots of the equation will move to form a curvilinear trajectory. So what is this trajectory? In this paper, we discuss the problem and get many wonderful conclusions Proposition 1 The above trajectory is Hyperbolic (limit