HP 48gx

Lesson 19: Finding all Roots of a Polynomial
A polynomial has the same number of roots as its degree—although
not all of these roots will be real or unique. The HP 48 offers an easy
way to numerically calculate all roots—both real and complez—of a
polynomial. The coefficients of the polynomial may be either real or
complex.
Example: Find all roots of 2° + 2% + 223 — 522 + 32 — 6.
Step 1: Fix the display to two decimal places and then choose the
Solve poly... from the SOLVE choose list.
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EEE SOLVE AM-H M+... +A1-H+A0 SEEEE
COEFFICIENT: [ AM i Al AO 1:
ROOTS:
ENTER COEFFICIENTS OR PRESS SOLVE
EMT] | | [SVME[SOLVE]
Step 2: Enter the coefficients of the polynomial, beginning with the
coefficient of the highest degree. Press between each
coefficient.
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FEE SOLVE AN-R N+. +RL-Hen0 SHEE
COEFFICIENTS [ AM .. AL AO I:
[112-323-6861
ROOTS:
ENTER ROOTS OR PRESS SOLVE
ET | | [SYME[SOLVE]
Step 3: Solve the polynomial.
SERE SOLVE AN-RSN+.+RL-Reno SEE
COEFFICIENTS [ AM. AL AD I:
[112-223-6861
ENTER ROOTS OR PRESS SOLVE
EMT] | | [SVYME[SOLVE
Solving Equations 5-9