Question

如果x四次方+mx三次方+nx-16有因式x²-3x+2,则m于n的值

Answer 1

设 x^4+m*x^3+n*x-16=(x^2-3*x+2)*（x^2+ax+b)

所以 x^4+m*x^3+n*x-16=x^4+(a-3)*x^3+(b-3a+2)*x^2+(2a-3b)*x+2b

则a-3=m

b-3a+2=0

2a-3b=n

2b=-16

所以b=-8 b-3a+2=0 a=2

则m=-1 n=26