问题
解答题
解方程x4+5x3-7x2-8x-12=0.
答案
左式=(x4+5x3-6x2)-(x2+8x+12)
=(x+6)[x2(x-1)-(x+2)]
=(x+6)(x3-x2-x-2)
=(x+6)[(x3-2x2)+(x2-x-2)]
=(x+6)(x-2)(x2+x+1)=0
可得原方程的四根为:
x1=-6,x2=2,x3=
,x4=-1+
i3 2 -1-
i3 2
解方程x4+5x3-7x2-8x-12=0.
左式=(x4+5x3-6x2)-(x2+8x+12)
=(x+6)[x2(x-1)-(x+2)]
=(x+6)(x3-x2-x-2)
=(x+6)[(x3-2x2)+(x2-x-2)]
=(x+6)(x-2)(x2+x+1)=0
可得原方程的四根为:
x1=-6,x2=2,x3=
,x4=-1+
i3 2 -1-
i3 2