一元三次方程求根公式
一元三次方程![](https://wkrtcs.bdimg.com/rtcs/image?w=101&md5sum=a9d78f99dd0e2bba032635eafdbbb24b&sign=ada3fded13&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=39&ipr={"t":"img","w":"101","h":"24","dataType":"gif","c":"word/media/image1.png"})
,根的判别式：。
当![](https://wkrtcs.bdimg.com/rtcs/image?w=15&md5sum=a9d78f99dd0e2bba032635eafdbbb24b&sign=ada3fded13&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=39&ipr={"t":"img","w":"15","h":"17","dataType":"gif","c":"word/media/image3.png"})
＞0时，公式①：
![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=a9d78f99dd0e2bba032635eafdbbb24b&sign=ada3fded13&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=39&ipr={"t":"img","w":"16","h":"23","dataType":"gif","c":"word/media/image4.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=19&md5sum=a9d78f99dd0e2bba032635eafdbbb24b&sign=ada3fded13&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=39&ipr={"t":"img","w":"19","h":"23","dataType":"gif","c":"word/media/image6.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=17&md5sum=a9d78f99dd0e2bba032635eafdbbb24b&sign=ada3fded13&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=39&ipr={"t":"img","w":"17","h":"24","dataType":"gif","c":"word/media/image8.png"})
其中，![](https://wkrtcs.bdimg.com/rtcs/image?w=91&md5sum=a9d78f99dd0e2bba032635eafdbbb24b&sign=ada3fded13&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=39&ipr={"t":"img","w":"91","h":"45","dataType":"gif","c":"word/media/image10.png"})
，。
当=0时，公式②：
当＜0时，公式③：
其中，![](https://wkrtcs.bdimg.com/rtcs/image?w=148&md5sum=a9d78f99dd0e2bba032635eafdbbb24b&sign=ada3fded13&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=39&ipr={"t":"img","w":"148","h":"51","dataType":"gif","c":"word/media/image18.png"})
。
当![](https://wkrtcs.bdimg.com/rtcs/image?w=29&md5sum=a9d78f99dd0e2bba032635eafdbbb24b&sign=ada3fded13&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=39&ipr={"t":"img","w":"29","h":"17","dataType":"gif","c":"word/media/image19.png"})
0时，方程有一个实根和一对共轭复根，
当0时，方程有三个实根，其中有两个根相等，
当＜0时，方程有三个不相等的实根。
对于一般的一元三次方程![](https://wkrtcs.bdimg.com/rtcs/image?w=145&md5sum=a9d78f99dd0e2bba032635eafdbbb24b&sign=ada3fded13&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=39&ipr={"t":"img","w":"145","h":"21","dataType":"gif","c":"word/media/image20.png"})
，等式两边同时除以三次项系数，得：，再令，可以消去二次项化成的形式，其中：，。
一元三次方程根与系数的关系：
++=,·+·+·=，··=。
本文来源：https://www.2haoxitong.net/k/doc/6c58edaa51e79b8968022664.html
文档为doc格式