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## The FZERO Function

The `fzero` function tries to find a root of a function near an initial value that you supply. First, define a function that can be passed as an argument to the `fzero` function. Then, call `fzero` to find the roots.

`    >> fzero( 'my_function', x0 )`

The above command finds the x value that is nearest to the value in `x0` that will cause the function computed by `my_function` to return a value of zero.

The `fzero` function can also be called with a string of characters that represents the function to be evaluated, instead of defining a new function.

`    >> fzero( '-x^2+10' , 3 )`

The `fzero` function can also be called with a range of x values that limits the range to search for a valid root.

`    >> fzero( '-x^2+10' , [3 5] )`

The `fzero` function can also be called to find the root of a polynomial using the `polyval` command. Use the following command to find the root of $y={x}^{3}+2{x}^{2}+3x+4$:

`    >> fzero( 'polyval([1 2 3 4],x)', 0 )`

It is also possible to find the root of a function that requires more than one input, if only one of the inputs to the function is a variable. For example, let's say we want to find where a polynomial crosses the x-axis and the coefficients of our polynomial are stored in the vector `c`. The command to evaluate the polynomial for a value in `x` is `polyval(c,x)`. We can find the roots of this polynomial with this syntax:

`    >> fzero( @(x)polyval(c,x), x0 )`

The `@(x)` piece indicates that we wish to treat `x` as the variable in the function `polyval(c,x)`. The `x0` argument is still the initial guess for the root of this function. Note: Be sure that `c` has been assigned its desired value before executing this command.