HP 48gII User Manual
Page 208
Page 6-7
Press
` to return to stack. The stack will show the following results in ALG
mode (the same result would be shown in RPN mode):
To see all the solutions, press the down-arrow key (
˜) to trigger the line
editor:
All the solutions are complex numbers: (0.432,-0.389), (0.432,0.389), (-
0.766, 0.632), (-0.766, -0.632).
Note: Recall that complex numbers in the calculator are represented as
ordered pairs, with the first number in the pair being the real part, and the
second number, the imaginary part. For example, the number (0.432,-0.389),
a complex number, will be written normally as 0.432 - 0.389i, where i is the
imaginary unit, i.e., i
2
= -1.
Note: The fundamental theorem of algebra indicates that there are n solutions
for any polynomial equation of order n. There is another theorem of algebra
that indicates that if one of the solutions to a polynomial equation with real
coefficients is a complex number, then the conjugate of that number is also a
solution. In other words, complex solutions to a polynomial equation with real
coefficients come in pairs. That means that polynomial equations with real
coefficients of odd order will have at least one real solution.
Generating polynomial coefficients given the polynomial's roots
Suppose you want to generate the polynomial whose roots are the numbers
[1, 5, -2, 4]. To use the calculator for this purpose, follow these steps:
‚Ϙ˜@@OK@@
Select Solve poly…
˜„Ф1‚н5
‚н2\‚н 4@@OK@@ Enter vector of roots
@SOLVE@
Solve
for
coefficients