HP HP-15C - Appendix B Stack Lift and the LAST X Register; Digit Entry Termination

Appendix: Accuracy of Numerical Calculations 207
If d ^ 0, then the roots are real numbers x and y calculated by
s — b + \fd sgn(6)
x — s / a
c/s
0
ifs^O
ifs = 0.
The s calculation avoids destructive cancellation.
When a = 0 ^ b, the larger root x, which should be °°, encounters
division by zero (Error 0) that can be cleared by pressing | R+ | three
times to exhibit the smaller root y correctly calculated. But when
all three coefficients vanish, the Error 0 message signals that both
roots are arbitrary.
The results of several cases are summarized below.
c
b
a
Roots
c
b
a
Roots
Case 1 Case 2
3 4
2 0
1 1
Real Complex
3 0±2i
1
Case 5
46,152,709
735,246
11,713
Real
62.77179203
62.77179203
Case 3 Case 4
1 654,321
1 654,322
10"13 654,323
Real Real
2X1013 0.9999984717
0.5 0.9999984717
Case 6
12,066,163
987,644
80,841
Complex
12. 21 711 755 ±/0.001 377461