题目

高分求三个一元六次方程的六个根
(1)x^6-10x^5+10x^4+80x^3-11x^2-70x=0
(2)x^6-6x^5-257x^4+750x^3+18544x^2+3936x-177408=0
(3)x^6-x^5-22x^4+35x^3+13x^2-22x-8=0

提问时间：2021-02-10

答案

解:(1)x^6-10x^5+10x^4+80x^3-11x^2-70x=(x-7)(x-5)(x-1)x(x+1)(x+2)=0
∴x1=7,x2=5,x3=1,x4=0,x5=-1,x6=-2
(2)x^6-6x^5-257x^4+750x^3+18544x^2+3936x-177408=(x-14)(x-12)(x-3)(x+4)(x+8)(x+11)=0
∴x1=14,x2=12,x3=3,x4=-4,x5=-8,x6=-11
(3)x^6-x^5-22x^4+35x^3+13x^2-22x-8=(x^3-5x^2+3x+2)(x^3+4x^2-5x-4)=0
解方程x^3-5x^2+3x+2=0得x1=4.164247938460211,x2=-0.3913823806309005,x3=1.22713444217069
解方程x^3+4x^2-5x-4=0得x4=1.4336646297832878,x5=-4.8595233886152185,x6=-0.574141241168071
∴x1=4.164247938460211
x2=-0.3913823806309005
x3=1.22713444217069
x4=1.4336646297832878
x5=-4.8595233886152185
x6=-0.574141241168071