Third Degree Polynomial Formula

The cubic formula is the closed-form solution for a cubic equation, i.e., it solves for the roots of a cubic polynomial equation. A general cubic equation is of the form ax³ + bx² + cx + d = 0 (third degree polynomial equation). The roots of this equation can be solved using the below cubic equation formula. The third degree polynomial equation formula displays the equation to solve three real roots (x1, x2 and x3) of the cubic equation.

Cubic Equation Formula:

x₁=(- term1 + r₁₃*cos(q³/3) )
x₂=(- term1 + r₁₃*cos(q³+(2*Π)/3) )
x₃=(- term1 + r₁₃*cos(q³+(4*Π)/3) )

Where,
discriminant(Δ) = q³ + r²
term1 = √(3.0)*((-t + s)/2)
r₁₃= 2 * √(q)
q = (3c- b²)/9
r = -27d + b(9c-2b²)
s = r + √(discriminant)
t = r – √(discriminant)