# Discriminant and Cubic Root Calculator

In algebra, the discriminant of a polynomial is a function of its coefficients. It provides details about the nature of its roots. Discriminant commonly expressed as 'D'. The number that multiplies by itself three times in order to create a cubic value is called as the cubic root or third root.

## Calculate the Discriminant, Cubic Root of Cubic Equations

In algebra, the discriminant of a polynomial is a function of its coefficients. It provides details about the nature of its roots. Discriminant commonly expressed as 'D'. The number that multiplies by itself three times in order to create a cubic value is called as the cubic root or third root.

Code to add this calci to your website

#### 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