若x^2+mx+n与x^3+2x-1的乘积中不含有x^3项和x^2项,求m,n的值

2025-03-02 03:08:05
推荐回答(1个)
回答1:

(x^2+mx+n)×(x^3+2x-1)
=x^5+mx^4+nx^3+2x^3+2mx^2+2nx-x^2-mx-n
=x^5+mx^4+x^3(n+2)+x^2(2m-1)+2nx-mx-n
∵x^2+mx+n与x^3+2x-1的乘积中不含有x^3项和x^2项
∴n+2=0 2m-1=0
∴n=-2 m=1/2