A simple algebra question for the program I am writing

Question

How can I decide:

-x ^ 3 - x - 4 = 0

You cannot use quadratic because it refers to third power, right?

I know that it should go out before ~ ​​1.3788, but I'm not sure how to get it.

I started with:

f (x) = x + (4 / (x ^ 2 + 1)).

Solution for 0, moving x to the other side, multiplying by (x ^ 2 + 1) on both sides, ultimately:

-x (x ^ 2 + 1) = 4,

or

-x ^ 3 - x - 4 = 0.

Answer 1

Finding the roots of equations using the Newton method or Fixed point iterative

Answer 2

Algebraically you want to use the Cardano method:

http://www.math.ucdavis.edu/~kkreith/tutorials/sample.lesson/cardano.html

, , .

, :

http://en.wikipedia.org/wiki/Cubic_function#Summary

Answer 3

cubic. , .

, .

? ? . "".

x ^ 3 + a2 * x ^ 2 + a1 * x + a0 = 0 (x-x1) * (x-x2) * (x-x3) = 0, x1, x2 x3 - . , , , , (x-x2) * (x-x3) = 0, , .

Answer 4

, newton (. ). (x-TheRootYouFound). , .

:

http://en.wikipedia.org/wiki/Newton%27s_method

http://en.wikipedia.org/wiki/Polynomial_long_division

. .

http://en.wikipedia.org/wiki/Root-finding_algorithm

Answer 5

, ...

, , x = i, , ( ). , , ( - , ), , , , . .

x = - . , .