Generally speaking, for the function f(x), if there is a real number c, when x=c, if f(c)=0, then x=c is called the zero point of the function f(x).

Solving the equation requires all zeros of f(x).

Suppose f(x) is continuous in the interval (x, y)

First, find out that A and B belong to the interval (x, y), which makes the signs of f(a) and f(b) different, that is to say, there must be zero in the interval (a, b), and then find out f[(a+b)/2].

Now suppose f (a)

(1) If f[(a+b)/2]=0, the point is zero.

If f [(a+b)/2]

Judgment of midpoint function value.

if f[(a+b)/2]>； 0, there are zeros in the interval (a, (a+b)/2) and (a+b)/2.

Judgment of midpoint function value.

In this way, it can always approach zero.

By reducing the cell where the zero point of f(x) is located by half at a time, the two endpoints of the interval gradually approach the zero point of the function, thus obtaining the approximate value of the zero point. This method is called dichotomy.

Find a way

Given the precision ξ, the steps of finding the approximate value of the zero point of the function f(x) by dichotomy are as follows:

1 determine the interval [a, b] and verify f (a) f (b)

Find the midpoint c of the interval (a, b).

3 calculate f (c).

(1) If f(c)=0, then c is the zero point of the function;

(2) If f (a) f (c)

(3) If f (c) f (b)

(4) it is judged whether the accuracy ξ is reached, that is, if┃┃┃┃┃┃┃┃┃┃┃.