ax^3+bx^2+cx+d=0 设三个重根为e 则可分解为a(x-e)^3=0 a(x^3-3ex^3+3e^2x-e^3)=0 ax^3-3aex^3+3ae^2x-ae^3=0 比较系数得b=-3ae,c=3ae^2,d=-ae^3 bc=-9a^2*e^3=9ad 则有三个相等的根的条件为bc=9ad