Examples: The Q-D Method
The examples below demonstrate how to use the Q-D metho program.
Real Roots Example
Find the approximate roots of the polynomial
Procedure |
Press |
Display |
|---|---|---|
|
|
||
| Select the program. | [ RUN ] { MTH } { --> } { ZRO } { Q-D } |
 |
| Enter the number of iterations | 40 { #it } { EOD } |  |
| Select new polynomial | { YES } |  |
| Enter the degree of the polynomial | 4 { n } { EOD } |  |
| Enter the coefficients | 4 { ENT } |  |
| 32 [ +/- ] { ENT } |  |
|
| 85 { ENT } |  |
|
| 93 [ +/- ] { ENT } |  |
|
| 36 { ENT } |  |
|
| Proceed with program | { NO } |  |
| { NXT } |  |
|
| { NXT } |  |
|
| { NXT } |  |
|
| { NXT } |  |
|
| { NXT } |  |
|
| { NXT } |  |
|
| { NXT } |  |
|
| { NXT } |  |
|
| Compute r and s values | { r/s } |  |
| Specify first and second roots to generate r and s | 1 { 1st } |  |
| 2 { 2nd } |  |
|
| View r and s | { EOD } |  |
| { NXT } |  |
|
The approximate roots are q1, q2, q3, and q4. The actual roots are 4, 1.5, 1.5, and 1, which could be determined by using more iterations or using this program's values for r and s with the Bairstow method program.
Complex Roots Example
Find the approximate roots of the polynomial
Procedure |
Press |
Display |
|---|---|---|
|
|
||
| Select the program. | [ RUN ] { MTH } { --> } { ZRO } { Q-D } |
 |
| Enter the number of iterations | 40 { #it } { EOD } |  |
| Select new polynomial | { YES } |  |
| Enter the degree of the polynomial | 4 { n } { EOD } |  |
| Enter the coefficients | 4 { ENT } |  |
| 20 [ +/- ] { ENT } |  |
|
| 25 { ENT } |  |
|
| 45 [ +/- ] { ENT } |  |
|
| 36 { ENT } |  |
|
| Proceed with program | { NO } |  |
| { NXT } |  |
|
| { NXT } |  |
|
| { NXT } |  |
|
| { NXT } |  |
|
| { NXT } |  |
|
| { NXT } |  |
|
| { NXT } |  |
|
| { NXT } |  |
|
| Compute r and s values | { r/s } |  |
| Specify second and third roots to generate r and s | 2 { 1st } |  |
| 3 { 2nd } |  |
|
| View r and s | { EOD } |  |
| { NXT } |  |
|
The approximate roots are q1, q2, a3, and q4. The actual roots are 4, 1.5i, -1.5i, and 1, which could be determined using this program's values for r and s with the Bairstow method program.
☚ Back