HP 48gII Graphing Calculator Manuel d'utilisateur télécharger pdf (Page 208)

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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

= -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:

‚Ï˜˜@@OK@@ Select Solve poly…

˜„Ô1‚í5

‚í2\‚í 4@@OK@@ Enter vector of roots

@SOLVE@ Solve for coefficients

1 2 ... 203 204 205 206 207 208 209 210 211 212 213 ... 863 864

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HP 48gII Graphing Calculator Manuel d'utilisateur Page 208

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