已知(x2+px+8)与(x2-3x+q)的乘积中不含x3和x2项,求p、q的值.
∵(x2+px+8)(x2-3x+q)
=x4-3x3+qx2+px3-3px2+pqx+8x2-24x+8q
=x4+(p-3)x3+(q-3p+8)x2+(pq-24)x+8q.
∵乘积中不含x2与x3项,
∴p-3=0,q-3p+8=0,
∴p=3,q=1.
已知(x2+px+8)与(x2-3x+q)的乘积中不含x3和x2项,求p、q的值.
∵(x2+px+8)(x2-3x+q)
=x4-3x3+qx2+px3-3px2+pqx+8x2-24x+8q
=x4+(p-3)x3+(q-3p+8)x2+(pq-24)x+8q.
∵乘积中不含x2与x3项,
∴p-3=0,q-3p+8=0,
∴p=3,q=1.