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On-line Solution of Univariate Cubic Equation


APP description

The standard one-dimensional cubic equation \(aX^3+bX^2+cX+d=0\)(a,b,c,d∈R, and a≠0), the solution is:

1.The Kardan formula method published by the Italian scholar Kardan in 1545;

2.The Sheng Jin formula method published by Chinese scholar Fan Shengjin in 1989.

Both formulas can solve the standard one-dimensional cubic equation. Due to the complexity of solving problems with the Caldan formula, the Shengjin formula is simple and clear, easy to remember, and the actual problem solving is more intuitive and more efficient.

Shengjin formula discrimination

When A = B = 0, the equation has a triple real root.

When\(Δ=B^2-4AC>0\), the equation has a real root and a pair of conjugate virtual roots.

When\(Δ=B^2-4AC=0\), the equation has three real roots, one of which has a double root.

When\(Δ=B^2-4AC<0\), the equation has three unequal real roots.

This calculator can help you dynamically calculate the roots of the cubic equation. Easy to understand and use.

Usage example

For example, enter a=1, b=8, c=16 and d=10. Click to solve the cubic equation

1x³ +8x² +16x+10d = 0

Click "Solve cubic equation" and output the result

Calculation results:

X1: -5.365230013414097 + 0

X2: -1.3173849932929516 + 0.3582593599240431

X3: -1.3173849932929516 + -0.3582593599240431


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