Finding all roots of a polynomial, Ifaiibiimiiiiiiiiibimiiaysiahnto, Finding all roots of a polynomial -10 – HP 48g Graphing Calculator User Manual
Page 216
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Finding All Roots of a Polynomial
A symbolic polynomial, such as
x.'^
+
ix'^ — 7x
+ 9, can also be
expressed as a vector of its coefficients: [ 1 4 — 7 9 ] . In this vector
form, very efficient numeric techniques can be applied to find a vector
of its roots.
To
use the polynomial
roc
■ Press
fi^fSOLVE) (5 (T]
■ finder:
to display the following:
18
i SOLVE
COEFFICIENTS t UN fll AO ]:
ROOTS:
ENTER COEFFICIENTS OR PRESS SOLVE
ifaiiBiimiiiiiiiiiBiMiiaysiaHnTO
To
find all roots ilynomial:
1. Open the polynomial root-finder.
2. Move the highlight to the CuEFFI
;3 field, if necessary.
3. Enter the polynomial in coefficient form. Use either the command
line (don’t forget the C ] delimiters)or the MatrixWriter. Note
that the first element in the vector should be the coefficient of the
highest order term and the last element should be the constant
term. Remember to include zeroes wherever “missing” terms are
located in the polynomial.
4. With the highlight located in the FiOuTS" field, press S O L V E . A
complex array of roots is displayed in the
FiUUTS”
field and a
labeled copy sent to the stack.
To find a
polynomial,
given a
set of
roots:
1. Open the polynomial root-finder.
2. Move the highlight to the ROOTS!! field, if necessary.
3. Enter the set of roots as a vector. Remember that if any of the
roots are complex, then you must enter ail roots as complex (real
roots are entered as <
real, B
)).
4. Move the highlight to the C O E F F I C I E N T S field and press S O L V E
18-10 Solving Equations