Question

已知2x2+10x+1=0,多项式(x+1)(x+2)(x+3)(x+4)的值为

Answer 1

5x^3-8x^2+x+4x^3+2mx^2-10x
=9x^3+(-8+2m)x^2-9x
∵相加后不含x的二次项
∴-8+2m=0
m=4
已知多项式5x³-8x²+x与多项式4x³+2mx²-10x相加后不含x的二次项，则m的值为__4___

Answer 2

2x2+10x+1=0
∴x²+5x=-1/2

(x+1)(x+2)(x+3)(x+4)
=[(x+1)(x+4)][(x+2)(x+3)]
=(x²+5x+4)(x²+5x+6)
=(-1/2+4)(-1/2+6)
=7/2×11/2
=77/4