1550078481-Ordinary_Differential_Equations__Roberts_

CSODE User's Guide

EXAMPLE Calculation of the Roots of a Cubic Polynomial

with Complex Coefficients

Find the roots of the cubic polynomial

x^3 + (-7 - 3i)x^2 + (10 + 15i)x + 8 - 12i = 0.

SOLUTION

503

In order to use POLYRTS to solve this equation, we double click the CSODE
icon and when the program selection screen appears on the monitor, we single
click on the POLYRTS button. Since the deg ree of the polynomial we wish
to solve is three, we enter 3 in the highlighted box after "N = " and press the
Enter key. Since the coefficient of x^3 in the polynomial is 1, we enter 1 in
the coefficient real part box for xA3. Then we enter - 7 in the coefficient real
part box and -3 in the coefficient imaginary part box for xA2. We enter 10 in
the coefficient real part box and 15 in the imaginary part box for xAl. Next,

we enter 8 in the coefficient real part box and -12 in the imaginary part box

for xAO. After making sure we have entered the values correctly, we click on
the VERIFY COEFFICIENTS/CALCULATE ROOTS button. When the
Please Confirm yes/no box appears, we click yes, since the coefficients are
entered correctly. This causes the screen shown in Figure A.5 to appear on
the monitor.
,.. POLYATS l!IJj]EJ
POLYRTS finds all zetos of a polynomiel wilh complex coefficienls of degree N where 1 <• N <· 10
Enter the de1:1ree of the polynomiel N • f3 (Afler you have entered the value o/ N. preS'S lhe Enter key.)
COEFFICIENTS
(Enter non·zeto coefficients.)
Term Real Patt Imaginary Part
•• 3

DBGRBB L OOOOOOBtOO RBAL PART IMAGINAR0. OOOOOOB+OO Y PART

-? l... 0000001+00 OOOOOOBtOl. -3. l. 0000008+00 SOOOOOB+OJ.

8. OOOOOOBtOO -l. ZOOOOOR+OJ.
   x ... 2 .7

•• (^0) ZJHl.O IHAC.INARY PART
-73.. 4J.463SB-.l OOOOOOB+OO 7 l2.. OOOOOOB+OO OOOOOOE+OO

4. OOOOOOE+OO -4. 44089ZB-J.6

Figure A.5 Screen Showing Coefficients and Roots

of a Third Degree Polynomial