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.

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Formula:

p = (1/3) [(3c/a) - (b2) / a2) ] q = (1/27) [ (2b3 / a3) - (9bc / a2) + (27e / a) ] D = (p/3)3 + (q/2)2 If D value is greater than 0: u = [ (-q/2) + D1/2 ] 1/3 v = [ (-q/2) - D1/2 ] 1/3 x = u+v s = [- (u+v)/2 ] t = [(u-v / 2) * 31/2] 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

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