一元四次方程求根公式

一元四次方程一般式：ax4+bx3+cx2+dx+e=0（a≠0,a,b,c,d,e∈R） p=-(3b2-8ac) q=3b4+16a2c2-16ab2c+16a2bd-64a3e

r=-(b3-4abc+a2d) 2

A=p2-3q B=pq-9r C=q2-3pr

若A=B=0

y1=y2=y3=-p/3=-q/p=-3r/q

x1=1/4a(-b+√y1+√y2+√y3) X3=1/4a(-b+√y1-√y2-√y3) X2=1/4a(-b-√y1+√y2-√y3) X4=1/4a(-b-√y1-√y2+√y3)

若B2-4AC=0

y1=-p+k y2=y3=-k/2

x1=1/4a(-b+√y1+√y2+√y3) X3=1/4a(-b+√y1-√y2-√y3) X2=1/4a(-b-√y1+√y2-√y3) X4=1/4a(-b-√y1-√y2+√y3) 若B2-4AC

T=(2Ap-3B)/(2A1.5 )

y1=-1/3(p+2Acos(1/3ArccosT))

y2=-1/3(p+2Acos(1/3ArccosT+2π/3))

y3=-1/3(p+2Acos(1/3ArccosT-2π/3))

x1=1/4a(-b+√y1+√y2+√y3)

X2=1/4a(-b-√y1+√y2-√y3)

X3=1/4a(-b+√y1-√y2-√y3)

X4=1/4a(-b-√y1-√y2+√y3)

若 B2-4AC >0