问题
填空题
若(x2+mx+n)(x2-3x+2)中,不含x2和x3项,则m=______,n=______.
答案
∵(x2+mx+n)(x2-3x+2),
=x4-3x3+2x2+mx3-3mx2+2mx+nx2-3nx+2n,
=x4+(-3+m)x3+(2-3m+n)x2+(2m-3n)x+2n,
又∵结果中不含x2和x3项,
∴-3+m=0,2-3m+n=0,
解得:m=3,n=7.
若(x2+mx+n)(x2-3x+2)中,不含x2和x3项,则m=______,n=______.
∵(x2+mx+n)(x2-3x+2),
=x4-3x3+2x2+mx3-3mx2+2mx+nx2-3nx+2n,
=x4+(-3+m)x3+(2-3m+n)x2+(2m-3n)x+2n,
又∵结果中不含x2和x3项,
∴-3+m=0,2-3m+n=0,
解得:m=3,n=7.