Question

Cho đa thức A=n^5-5n^3+4n.Tim nghiệm đa thức A

Answer 1

Ta có: \(\left\{{}\begin{matrix}A=n^5-5n^3+4n\\A=0\end{matrix}\right.\Rightarrow n^5-5n^3+4n=0\)

\(\Leftrightarrow n\left(n^4-5n^2+4\right)=0\)

\(\Leftrightarrow n\left(n^4-4n^2-n^2+4\right)=0\)

\(\Leftrightarrow n\left[n^2\left(n^2-4\right)-\left(n^2-4\right)\right]=0\)

\(\Leftrightarrow n\left(n^2-1\right)\left(n^2-4\right)=0\)

\(\Leftrightarrow n\left(n-1\right)\left(n+1\right)\left(n-2\right)\left(n+2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}n=0\\n=\pm1\\n=\pm2\end{matrix}\right.\)