若(x²+nx+3)(x²-3x+m)的乘积甲不含x²项和x³项,求m、n的值

问题描述:

若(x²+nx+3)(x²-3x+m)的乘积甲不含x²项和x³项,求m、n的值

(2)(x2+nx+3)(x2-3x+m)
=x4+nx3+3x2-3x3-3nx2-9x+mx2+mnx+3m
=x4+(n-3)x3+(3-3n+m)x2+(mn-9)x+3m,
∵乘积中不含x2和x3项,
∴n-3=0,3-3n+m=0,
解得:m=6,n=3.