Can Newton's iterative method be used to find all roots of equation of degree n with one variable For example, for a cubic equation with one variable, if the three roots are different, only one real root can be found by Newton iteration method. How can the other two roots be found? If there are complex roots, can we find them? But the iterative method is to find the numerical solution, and sometimes the equation is transcendental equation, can not do polynomial division.

Can Newton's iterative method be used to find all roots of equation of degree n with one variable For example, for a cubic equation with one variable, if the three roots are different, only one real root can be found by Newton iteration method. How can the other two roots be found? If there are complex roots, can we find them? But the iterative method is to find the numerical solution, and sometimes the equation is transcendental equation, can not do polynomial division.

After a root comes out, for example, if it is set to a, it can be removed without (x-a). Because it is the root of polynomial agenda, it can be completely removed. In this way, it becomes a polynomial of lower degree. The remaining root must be in the polynomial equation of lower degree. The numerical solution is an approximation of the real solution, which has errors

The relationship between the root and coefficient of cubic equation with one variable?
Q: "a, B and C are the three roots of the equation X3 + PX + q = 0. From the relationship between roots and coefficients, we know that a + B + C = 0."
Why is it? [words in quotation marks are from the book]

Suppose that the roots of the equation are a, B, C (the cubic equation has three roots), then the equation can be written as (x-a) (X-B) (x-C) = 0, and then split the equation: X3 - (a + B + C) x2 + (AB + AC + BC) x-abc = 0. Compared with the original equation, we can see that a + B + C = 0 (the coefficient in front of the quadratic term of the original equation is 0!)
This method can be used for the relationship of general coefficients:)

A quadratic equation of one variable with a root of 0, write such an equation

The square of x = 0