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Discriminant and Cubic Root Formula - Polynomial Equation Solver
Calculator
Formula
Formula:
p = (1/3) [(3c/a) - (b
2
) / a
2
) ]
q = (1/27) [ (2b
3
/ a
3
) - (9bc / a
2
) + (27e / a) ]
D = (p/3)
3
+ (q/2)
2
If D value is greater than 0:
u = [ (-q/2) + D
1/2
]
1/3
v = [ (-q/2) - D
1/2
]
1/3
x = u+v
s = [- (u+v)/2 ]
t = [(u-v / 2) * 3
1/2
]
y = s+t
z = s-t
If D value is less than 0:
Φ = acos [ (-q/2) (|p| / 3)
-3/2
]
x = 2 [ (|p| / 3)
1/2
cos (Φ/3) ]
y = -2 [ (|p| / 3)
1/2
cos (Φ + π)/3 ]
z =-2 [ (|p| / 3)
1/2
cos (Φ - π)/3 ]
Where,
D = Discriminant
p,q = Real Constant
a,b,c,e = Real Constant
x,y,z = Cubic root
u,v = Real Constant
s,t = Temp Variable
cos = Cosine
Φ = Angle
Related Calculator:
Discriminant and Cubic Root Calculator
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