Question

x^3+2x^2+1=0怎么因式分解啊?目测是有复数的……

Answer 1

一元三次方程x^3+a1x^2+a2x+a3=0求根公式(又称卡丹公式),公式为:设p=-(a1^2/3)+a2,q=2a^3/27-a1a2/3+a3有

x1=[-q/2-(q^2/4+p^3/27)^(1/2)]^(1/3)+[-q/2+(q^2/4+p^3/27)^(1/2)]^(1/3)=u+v

x2=-1/2(u+v)+i/3^(1/2)*(u-v)

x3=-1/2(u+v)-i/3^(1/2)*(u-v)

所以结果为(x-x1)(x-x2)(x-x3)