Can you give us any more details about the function? For a completely general function, this sort of thing is not really possible. However if you have a specific class of functions you are interested in (such as polynomials) then it may be possible.

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Well I’ll give you a hint.

You know (or should know) that sin(x) is always between -1 and 1. Given this, you should be able to calculate a range of x values where that function could possibly have roots.

Once you’ve done that, you can use what you know about where the roots of sin(x) are to estimate how many roots your function could have and ranges where they could be.

I found the method “Bracketing method” in the following link

It works fine for my purpose. Thanks to all.

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For a function, I want to calculate the range where one root exists. For example, f(x) has a root in subrange [a1,b1], another root in subrange[a2,b2] in a total range of [X,Y]. Is any such algorithm available to calculate the ranges?

Thanks in advance.