Using the root Function

Mathcad root function is designed to find roots of functions, one root at a time. Here is an example of how to use it:

define a function you seek a root of, for example

make a guess for the root's value, for example

call the root function with the function and the guess as arguments:

display the result:

check the result:

Before trying to find a root, it is a good idea to know something about the function for which the root is being sought. A function may have more than one root and, in order to find all of them without just making random guesses, a graph is often necessary. By graphing a function, you can make approximations for the values of the real roots. Here are some steps to follow for finding all the roots of a given function in a given interval:

Plot the function f(x) over the range (0,10).

Examine where the graph crosses the x axis. This shows how many
roots the function has in the range being plotted. Changing the axes style of

the graph could be very helpful in locating the roots of the function. Double-click on the graph or choose Graph / XY Plot from the Format menu to open a tabbed dialog box. Click on the X-Y Axes tab, then select the Crossed style.

There are three distinct places where the graph of the function, f(x), crosses the
x axis. We found one root already:

Another root seems to be close to 4. Therefore, the guess should be

Define a variable in terms of the root function and look at the result.

So, the root is at approximately 3.927.

The last root can be found in similar fashion.

Incorrect Calls to root

The following calls to root are incorrect:

You must pass the function and its arguments as F(t), not just the name of the function, F.

The second argument must be a variable name defined as the guess, not the guess value itself.

The name of the guess and the function variable do not match.

The second argument is not a valid Mathcad variable name. The subscript here was entered with [.