若(x2+ax+8)(x2-3x+b)的积中不含x2项和x3项,则a=_,b=_.

问题描述:

若(x2+ax+8)(x2-3x+b)的积中不含x2项和x3项,则a=______,b=______.

(x2+ax+8)(x2-3x+b)=x4-3x3+bx2+ax3-3ax2+abx+8x2-24x+8b=x4+(a-3)x3+(b-3a+8)x2+(ab-24)x+8b,
∵积中不含x2项和x3项,
∴a-3=0,b-3a+8=0,
解得:a=3,b=1.
故答案为:3;1