Question

已知(x^2-3x+m)(x-n)=x^3-2x+21,则m=(),n=()

Answer 1

(x²-3x+m)(x-n)
=x³-nx²-3x²+3nx+mx-mn
=x³-(n+3)x²+(3n+m)x-mn
=x³-2x+21
即n+3=0
3n+m=-2
-mn=21
解得
n=-3
m=7

Answer 2

已知(x^2-3x+m)(x-n)=x^3-2x+21=x³-nx²-3x²+3nx+mx-mn,则m=(7),n=(-3)
-n-3=0;
n=-3;
3n+m=-2;
m=7;
如果本题有什么不明白可以追问，如果满意记得采纳
如果有其他问题请采纳本题后另发点击向我求助，答题不易，请谅解，谢谢。
祝学习进步

Answer 3

(x^2-3x+m)(x-n)=x^3-2x+21,
(x^2-3x+m)(x-n)
= x^3 -3x²+mx -nx² +3nx -mn
= x^3 - (3+n) x² +(m+3n)x -mn
=x^3-2x+21,
3+n = 0 n = -3
m+3n = -2 7-9=-2
mn=-21 m=7

则m=(7),n=(-3)

Answer 4

(x^2-3x+m)(x-n)=x^3-nx^2-3x^2+3nx+mx-mn=x^3-(n+3)x^2+(3n+m)x-mn
=x^3-2x+21,
故有n+3=0,3n+m=-2,mn=-21
解得m=7,n=-3