已知x^4+ax^2+1能被x^2+ax+1整除,确定a的值
1个回答
用分式除法做
x^2 -ax +(a-1+a^2)
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x^2+ax+1 | x^4+ ax^2 +1
|
| x^4+ax^3 +x^2
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| -ax^3 +(a-1)x^2 +1
| -ax^3 -a^2x^2 -ax
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| (a-1+a^2)x^2 +ax +1
| (a-1+a^2)x^2+(a-1+a^2)ax +(a-1+a^2)
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0
∵整除
∴a=(a-1+a^2)a 1=a-1+a^2
a^2+a-2=0
(a+2)(a-1)=0
a=-2 或a=1
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