# How to find zeros of a function?

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Wenjie on 17 Dec 2018
Answered: Alexander on 25 Feb 2024
For instance,
x = -3.55:0.1:3.55;
y = x.^2 - 4;
Obviously, when x=2 or -2, y=0.
But I want to know how to use matlab to find zeros of a function y = f(x) when x is a matrix defined by the user like the above case.
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Mark Sherstan on 17 Dec 2018
As per documentaiton note:
x = fzero(fun,x0) tries to find a point x where fun(x) = 0. This solution is where fun(x) changes sign—fzero cannot find a root of a function such as x^2.
Akira Agata on 17 Dec 2018
If your function is always polynomial, you can use roots function to do this task. Please look at the following help page.

Walter Roberson on 17 Dec 2018
x(y==0)
Note that this can miss an indefinite number of zeroes of a function if the x do not happen to sample at the right places . It also will not detect zero crossings between x values . You could make use of the results to get hints about zero crossings .

Wenjie on 17 Dec 2018
I've found the solution. First, define the function in a separate file as
function y = fun(x)
y = x.^2-4;
end
Then use fzero to find x value that will give y=0.
x0 = fzero(@(x) fun(x), 3)
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Nico on 25 Feb 2024
What does the @(x) and the 3 mean? Sorry I'm university student with no experience...
Dyuman Joshi on 25 Feb 2024
Edited: Dyuman Joshi on 25 Feb 2024
@(x) is the syntax used to define a Function Handle / Anonymous Functions
The 3 is provided as an initial guess for fzero() to work with - see fzero for more information.

Alexander on 25 Feb 2024
If it's not a function but meassured data I would go like this in a first try:
x = -3.55:0.0001:3.55; % assuming 10 kHz sample frequency
y = x.^2 - 4;
yS = sign(y);
dyS = diff(yS);
Z=find(dyS ~= 0);
x(Z)