Hp 50g Graphing Calculator Instrukcja Użytkownika Pobierz pdf (Strona 213)

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All the solutions are complex numbers: (0.432,-0.389), (0.432,0.389), (-0.766,

0.632), (-0.766, -0.632).

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

Press ` to return to stack, the coefficients will be shown in the stack.

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.

1 2 ... 208 209 210 211 212 213 214 215 216 217 218 ... 886 887

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