HP 49g+ - Manual (Page 205)

Page 6-8
Press
` to return to stack, the coefficients will be shown in the stack.
Press
˜ to trigger the line editor to see all the coefficients.
Note: If you want to get a polynomial with real coefficients, but having
complex 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 resulting polynomial will have complex 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'.