Cubic Equation Calculator

For example: input a=1, b=8, c=16 d=10。
ax3 + bx2 + cx + d = 0
x3 + x2 + x+ d = 0
X1: +   i
X2: +   i
X3: +   i

The standard cubic equation aX^3+bX^2+cX+d=0 (a, b, c, d∈R, and a≠0) has two solutions: 1. The Cardan formula method published by Italian scholar Cardan in 1545; 2. The Shengjin formula method published by Chinese scholar Fan Shengjin in 1989.

Both formula methods can solve the standard cubic equation. Due to the complexity of solving problems with the Cardan formula, the Shengjin formula is concise and clear, easy to remember, and more intuitive and efficient in actual problem solving.

Shengjin formula identification method

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 imaginary roots.

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

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