Enter the coefficients of a cubic equation to calculate one real root using Cardano’s formula. This calculator is designed to find one real root for cubic equations of the form ax^3 + bx^2 + cx + d = 0.
Cardano’s Formula
The formula used to calculate one real root of a cubic equation is as follows:
x = sqrt[3]{-frac{g}{2} + sqrt{frac{g^2}{4} + frac{f^3}{27}}} + sqrt[3]{-frac{g}{2} - sqrt{frac{g^2}{4} + frac{f^3}{27}}} - frac{b}{3a}
Where:
- f = (3c/a) – (b^2/a^2)/3
- g = (2b^3/a^3) – (9bc/a^2) + (27d/a)/27
- h = g^2/4 + f^3/27
To calculate one real root of the cubic equation, follow these steps:
How to Calculate a Root Using Cardano’s Formula?
The following steps outline how to calculate one real root of a cubic equation using Cardano’s formula.
- First, determine the coefficients of the cubic equation (a, b, c, d).
- Next, calculate the values of f, g, and h using the coefficients.
- Check if the discriminant h is greater than 0. If so, proceed to calculate the real root.
- Calculate the real root using the formula above.
- Use the calculator above to verify your result.
Example Problem:
Use the following coefficients as an example problem to test your knowledge.
Coefficient a = 1
Coefficient b = -6
Coefficient c = 11
Coefficient d = -6
