我们知道一元二次方程的根的情况可以用判别式来判断,那么一元三次方程的根的情况又如何判断呢?要解决这个问题,只要根据函数的单调性与极值,画出函数简图,即可由图象与X轴交点个数得到对应方程的根的情况,因此可以用导数来研究。三次函数的导函数为二次函数,所以三次函数的许多性质可以借助二次函数来研究。 We know that the root of a quadratic equation can be judged by a discriminant, so how does the root of a ternary equation be judged? To solve this problem, draw a function diagram based on the monotonicity and extremum of the function. Therefore, the root of the corresponding equation can be obtained from the number of intersections between the image and the X-axis, so it can be studied by using the derivative. The derivative function of the cubic function is a quadratic function, so many properties of the cubic function can be studied by means of a quadratic function.