Question

已知x的4次幂+m乘x的3次幂+nx-16有因式（x-1)和（x-2),求m、n的值

Answer 1

解.设x4+mx3+nx-16=(x-1)(x-2)(x2+ax+b)=(x2-3x+2)(x2+ax+b)

得 2b=-16

b-3a+2=0

b=-8

a=-2

(x-1)(x-2)(x2-2x-8)=(x-1)(x-2)(x-4)(x+2)=x4-5x3+20x-16

∴m=-5 n=20