Question

xác định a,b,c,d biết

\(x^4+x^3-x^2+ax+b=\left(x^2+x-2\right)\left(x^2+cx+d\right)\)

Answer 1

Ta có: \(VP=\left(x^2+x-2\right)\left(x^2+cx+d\right)\)

\(=x^4+\left(c+1\right)x^3+\left(d+c-2\right)x^2+\left(d-2c\right)x-2d\)

Và \(VT=x^4+x^3-x^2+ax+b\)

Đồng nhất 2 đa thức trên ta có:

\(\left\{{}\begin{matrix}\left(c+1\right)x^3=x^3\\\left(d+c-2\right)x^2=-x^2\\\left(d-2c\right)x=ax\\-2d=b\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}c+1=1\\d+c-2=-1\\d-2c=a\\-2d=b\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}c=0\\d-2=-1\\d=a\\b=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}c=0\\d=1\\d=a\\b=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}a=d=1\\b=c=0\end{matrix}\right.\)