Question

x^2+mx+n)(x^2-2x-3)的乘积中不含x^3,x^2项,求m,n的值

Answer 1

先展开(x^2+mx+n)(x^2-2x-3)=x^4-2x^3-3x^2+mx^3-2mx^2-3mx+nx^2-2nx-3n,由于(x^2+mx+n)(x^2-2x-3)的乘积中不含x^3,x^2项,则-2x^3+mx^3=0; -3x^2-2mx^2+nx^2=0,解得m=2; n=7