Question

已知关于X的二次三项式3x∧2-mx+n分解因式的结果为(3x+2)(x-1),求的m,n值？

Answer 1

(3x+2)(x-1)
=3x^2+2x-3x-2
=3x^2-x+(-2)
所以m=1 n=-2,1,把他拆开是3x∧2+x-2 所以m=-1 n=-2,2,根据题意得:
3x+2=0
x1=-2/3
x-1=0
x2=1
将x1,x2代入后得方程组:
4/3-2m/3+n=0
3-m+n=0
整理得:
2m+3n=-4 (1)
-m+n=-3 (2)
(2)*2得:
2m+3n=-4 (1)
-2m+2n=-6 (3)
(1)+(3)得:
5n=-10
n=-2
解方程组得:
m=-1
n=-2,1,(3x+2)(x-1)=3x∧2-x-2所以m=1 n=-2,0,