Check if textbox contains invalid characters

I having a issue trying to check if a textbox only contains a-z 0-9 values using JavaScript.

I have a textbox on my page:

<input type="text" id="first_name" class="first_name" value="">

I am using the following JavaScript Function to check my textbox:

// Function to check letters and numbers
function alphanumeric(inputtxt)
{ 
//alert(inputtxt);
var letters = "/^[0-9a-zA-Z]+$/";
if(inputtxt.value.match(letters))
{
alert('accepted');
}
else
{
alert('Please input alphanumeric characters only');
return false;
}
}

And I am calling my function like this:

var test = alphanumeric(document.getElementById("first_name").value);

However nothing is happening.

If I alert 'inputtxt' in my alphanumeric function it returns my value I have in my textbox so I know there is a value to be checked, but it doesn't seem to go on from there.

Does anyone know where I have gone wrong?

I am trying to do this with JavaScript (no jQuery).