若x2+mx+n与x3+2x-1的乘积中不含有x3项和x2项,求m,n的值.

问题描述:

若x2+mx+n与x3+2x-1的乘积中不含有x3项和x2项,求m,n的值.

∵(x2+mx+n)(x2+2x-1)
=x4+2x3-x2+mx3-2mx2-mx+nx2+2nx-n
=x4+(2+m)x3+(-1-2m+n)x2+(-m+2n)x-n,
∴要使x2+mx+n与x3+2x-1的乘积中不含有x3项和x2项,
则有2+m=0,-1-2m+n=0,
解得m=-2,n=-3.