Question

xác định a,b sao cho: x^4+ax^2+b chia hết cho x^2 -x+1

Answer 1

=>x^4-x^3+x^2+x^3-x^2+x+ax^2-x+b chia het cho x^2-x+1

=>ax^2-x+b=0

=>a=0 va b=-1

Answer 2

\(x^4+ax^2+b=\left(x^2-x+1\right)\left(x^2+x+a\right)+\left(a-1\right)x+b-a\)

\(x^4+ax^2+b\) chia hết cho \(x^2-x+1\) 

\(\Rightarrow\left(a-1\right)x+b-a=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}a-1=0\\b-a=0\end{matrix}\right.\Leftrightarrow a=b=1\)