设f(x)=(1+a)x^4+x^3-(3a+2)x^2-4a,试证明对任意的实数a,方程f(x)=0总有相同实根

f(x)=(1+a)x^4+x^3-(3a+2)x^2-4af(x)=(x^4-3x^2-4)a+x^4+x^3-2x^2x^4-3x^2-4=(x^2+1)(x^2-4)=(x^2+1)(x-2)(x+2)x^4+x^3-2x^2=x^2(x^2+x-2)=x^2(x+2)(x-1)从而f(x)=(x^2+1)(x-2)(x+2)a+x^2(x+2)(x-1)=(x+2)[(x^2+1)(x...