解六阶多项式

发布网友发布时间：2024-05-09 18:27

共1个回答

热心网友时间：2024-08-10 00:23

用MATLAB的roots()函数
当y=5时，定义多项式p = 0.0285x6 - 0.8216x5 + 9.1725x4 - 49.286x3 + 128.48x2 - 158.88x + 171.37-5，
即
p=[0.0285 -0.8216 9.1725 -49.2860 128.4800 -158.8800 166.3700]
然后
r=roots(p)
得
r =
8.1912 + 0.3959i
8.1912 - 0.3959i
5.7551 + 2.1224i
5.7551 - 2.1224i
0.4677 + 1.4451i
0.4677 - 1.4451i
说明无实根,就是说当x为实数时y不可能等于5。
以下是用roots()计算出的当y=5,10,15,...,95时x的取值：
r1 =

8.1912 + 0.3959i
8.1912 - 0.3959i
5.7551 + 2.1224i
5.7551 - 2.1224i
0.4677 + 1.4451i
0.4677 - 1.4451i

r2 =

8.4542
7.7129
5.8409 + 2.0297i
5.8409 - 2.0297i
0.4895 + 1.4252i
0.4895 - 1.4252i

r3 =

8.6725
7.2144
5.9583 + 1.9325i
5.9583 - 1.9325i
0.5123 + 1.4045i
0.5123 - 1.4045i

r4 =

8.8043
6.6986
6.1265 + 1.8484i
6.1265 - 1.8484i
0.5361 + 1.3827i
0.5361 - 1.3827i

r5 =

8.9037
6.3409 + 1.8316i
6.3409 - 1.8316i
6.1206
0.5610 + 1.3597i
0.5610 - 1.3597i

r6 =

8.9850
6.5251 + 1.8974i
6.5251 - 1.8974i
5.6183
0.5873 + 1.3353i
0.5873 - 1.3353i

r7 =

9.0545
6.6529 + 1.9868i
6.6529 - 1.9868i
5.2379
0.6150 + 1.3094i
0.6150 - 1.3094i

r8 =

9.1156
6.7444 + 2.0728i
6.7444 - 2.0728i
4.9349
0.6444 + 1.2818i
0.6444 - 1.2818i

r9 =

9.1703
6.8145 + 2.1508i
6.8145 - 2.1508i
4.6773
0.6757 + 1.2522i
0.6757 - 1.2522i

r10 =

9.2201
6.8711 + 2.2212i
6.8711 - 2.2212i
4.4474
0.7092 + 1.2201i
0.7092 - 1.2201i

r11 =

9.2658
6.9183 + 2.2850i
6.9183 - 2.2850i
4.2346
0.7455 + 1.1851i
0.7455 - 1.1851i

r12 =

9.3081
6.9590 + 2.3433i
6.9590 - 2.3433i
4.0320
0.7850 + 1.1467i
0.7850 - 1.1467i

r13 =

9.3476
6.9946 + 2.3969i
6.9946 - 2.3969i
3.8340
0.8286 + 1.1038i
0.8286 - 1.1038i

r14 =

9.3847
7.0264 + 2.4465i
7.0264 - 2.4465i
3.6358
0.8774 + 1.0551i
0.8774 - 1.0551i

r15 =

9.4196
7.0551 + 2.4928i
7.0551 - 2.4928i
3.4317
0.9333 + 0.9987i
0.9333 - 0.9987i

r16 =

9.4527
7.0812 + 2.5361i
7.0812 - 2.5361i
3.2142
0.9993 + 0.9308i
0.9993 - 0.9308i

r17 =

9.4842
7.1053 + 2.5769i
7.1053 - 2.5769i
2.9700
1.0816 + 0.8446i
1.0816 - 0.8446i

r18 =

9.5142
7.1276 + 2.6155i
7.1276 - 2.6155i
2.6673
1.1957 + 0.7226i
1.1957 - 0.7226i

r19 =

9.5429
7.1484 + 2.6520i
7.1484 - 2.6520i
2.1338
1.4273 + 0.4759i
1.4273 - 0.4759i

y>=10时,均有两个实根