How do you find zeros of a function?

Answer 1

For simple functions, f(x), you set f(x) = 0 and solve that.

For example, to find the 0 of 3x + 7

you set 3x - 7 = 0

so that 3x = 7 or x = 7/3. That is the 0 of the function.

However, there are plenty of functions where this method will fail because the function cannot be solved algebraically.

Linear and quadratic functions are easy; cubics are possible but tedious. Bur what about something like

6x2 + ln(x) = 7sin(x) where x is measured in radians ?

You then go for numerical solutions. This entails finding one approximate solution. Use that solution to find a better one and then use that one to find a still better one and so on. Hopefully (though not always) the iteration will converge to a root. One of the better known methods for this is the Newton-Raphson method.

These methods work for functions that are continuous and differentiable, but many functions are not. And then you go into some serious mathematics and, in order to explain that, I need to know a lot more about your mathematical knowledge.