解方程:2x^4-3x^3-x^2-3x+2=0
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/19 23:17:44
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解方程:2x^4-3x^3-x^2-3x+2=0
解方程:2x^4-3x^3-x^2-3x+2=0
解方程:2x^4-3x^3-x^2-3x+2=0
答:
2x^4-3x^3-x^2-3x+2=0
(2x^4-4x^3)+(x^3-2x^2)+(x^2-3x+2)=0
2(x-2)x^3+(x-2)x^2+(x-1)(x-2)=0
(x-2)(2x^3+x^2+x-1)=0
所以:x-2=0或者2x^3+x^2+x-1=0
解得:x=2
2x^3+x^2+x-1=0
(2x^3-x^2)+2x^2+x-1=0
(2x-1)x^2+(2x-1)(x+1)=0
(2x-1)(x^2+x+1)=0
因为:x^2+x+1>0恒成立
所以:2x-1=0
解得:x=1/2
综上所述,方程的解为x1=1/2,x2=2
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