Cubic Equation Calculator

A cubic equation has the form ax3 + bx2 + cx + d = 0. It is defined as third degree polynomial equation. It must have the term in x3 or it would not be cubic but any or all of b, c and d can be zero. The solutions of this cubic equation are termed as the roots or zeros of the cubic equation. All third degree polynomial equations will have either one or three real roots. Solve the roots of the third degree equation using this cubic equation calculator.

Solve Third Degree Polynomial Equation

ax3 + bx2 + cx + d = 0 (For example, Enter a=1, b=8, c=16 and d=10)

x3 +
x2 +


X1: + i
X2: + i
X3: + i
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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)

This calculator will help you dynamically to calculate the roots of the cubic equation.

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