How to solve the cubic equation of one variable

The ordinary solution of cubic equation with one variable is very complicated. First, we need to remove the coefficients of x ^ 2 and x ^ 3, and then test the discriminant to determine whether it has one real root or three real roots. Then we use a formula called "Kadan formula" to solve the equation. Even the real solution of some equations must be expressed by imaginary numbers, And these contents are not even clear to many people who have studied complex numbers in senior three. Therefore, in middle school, we generally don't teach the solution of cubic equation of one variable
If you really want to take a cubic equation of one variable, first try to factorize it. A cubic polynomial of one variable can be factorized, and at least it can be decomposed into a (x-x1) (x ^ 2 + PX + Q). Therefore, factorization should be tried first
12200x ^ 2-90000x ^ 3-32 = 0 is not a good solution, his three solutions are - 2 / 45, 2 / 25, 1 / 10
In addition, we can also teach you a way to guess the root: if a rational number P / Q is the root of a polynomial equation with integral coefficients, then q is the divisor of the coefficient of the highest degree term and P is the divisor of the constant term

Solving a cubic equation with one variable
X3+2X2-x+2=0

The original formula X2 (X-2) - (X-2) = 0, then, (X-2) (x2-1) = 0, so the solution is 2, - 1, + 1

The detailed solution process of univariate cubic equation: (2 / D) + 1 / (D + 5) + 1 / (D + 12) - 1 / (D + 1) = 0?

The universal root formula of cubic equation with one variable given by fan Shengjin is called Shengjin formula（ http://baike.baidu.com/view/1382952.htm ）Solve the equation (2 / D) + 1 / (D + 5) + 1 / (D + 12) - 1 / (D + 1) = 0, let 1 / D = x, then d = 1 / x, and put it into the above formula to get the equation: 120x ^ 3 + 111x ^ 2 + 38x + 3 = 0

To solve a cubic equation of one variable,
x^3+3x^2--3X-9=0

x^3 - 3x + 3x^2 - 9 = 0
x(x^2 - 3) + 3(x^2 - 3)=0
(x+3)(x^2 - 3)=0
So x = - 2, √ 3, √ 3

How to solve the cubic equation of one variable