HP 50g Graphing Calculator - Manual (Page 214)

Page 6-8
Press ˜ to trigger the line editor to see all the coefficients.
Generating an algebraic expression for the polynomial
You can use the calculator to generate an algebraic expression for a
polynomial given the coefficients or the roots of the polynomial. The resulting
expression will be given in terms of the default CAS variable X. (The examples
below shows how you can replace X with any other variable by using the
function |.)
To generate the algebraic expression using the coefficients, try the following
example. Assume that the polynomial coefficients are [1,5,-2,4]. Use the
following keystrokes:
‚Ϙ˜
@@OK@@ Select Solve poly…
„Ф1‚н5 Enter vector of coefficients
‚н2\‚н 4
@@OK@@
—
@SYMB@ Generate symbolic expression
` Return to stack.
The expression thus generated is shown in the stack as:
'X^3+5*X^2+-2*X+4'.
To generate the algebraic expression using the roots, try the following example.
Assume that the polynomial roots are [1,3,-2,1]. Use the following keystrokes:
‚Ϙ˜
@@OK@@ Select Solve poly…
˜„Ф1‚н3 Enter vector of roots
‚н2\‚н 1
@@OK@@
˜
@SYMB@ Generate symbolic expression
` Return to stack.
The expression thus generated is shown in the stack as:' (X-1)*(X-3)*(X+2)*(X-1) '.
Note: If you want to get a polynomial with real coefficients, but having com-
plex roots, you must include the complex roots in pairs of conjugate numbers.
To illustrate the point, generate a polynomial having the roots [1 (1,2) (1,-
2)]. Verify that the resulting polynomial has only real coefficients. Also, try
generating a polynomial with roots [1 (1,2) (-1,2)], and verify that the result-
ing polynomial will have complex coefficients.