1. !
quot;#
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2. 1
3

3. ax + bx + c = 0
2
4

4. )
− b ± b − 4ac
2
x=
2a
5

5. )
∆ = b − 4ac
2
6

6. )quot; *
y
X1 X2
x
7

7. & * ) quot;(
Initial Request
1 Day
After
1 Week
After
8

8. & * ) quot;(
Initial Request Evolution Request
1 Day
After
Few Weeks Later
1 Day
1 Week
After
After
9

9. 1
10

10. )quot; &
j
X1 X2
x
11

11. & * ) quot;(
Initial Request
1 Day
After
1 Week
After
12

12. & * ) quot;(
Initial Request Evolution Request
1 Day Few Weeks Later
After
1 Day
1 Week
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After
13

13. 1
14

14. )& +* ,
y
X1 X2
x
X
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X
15

15. & * ) quot;(
Initial Request
1 Day
After
1 Week
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16

16. & * ) quot;(
Initial Request Evolution Request
1 Day
After
Few Weeks Later ?
1 Day
1 Week
After
After
17

17. 1
18

18. Start
Input coefficients a,b,c
Computes discriminant
Delta = b * b – 4 * a * c
<0
>0 Discriminant
Sign
=0
Computes roots Computes single root
print roots print root print no roots
End
19

19. 1
20

20. delta = (b*b) - (4*a*c); // discrimant computation
if (delta < 0.0) {
System.out.println (quot; No rootsquot;);
}
else if (delta > 0.0) {
System.out.println (quot; Two roots :quot;);
System.out.println (quot; x1 = quot; + (-b + Math.sqrt(delta))/ (2.0 * a));
System.out.println (quot; x2 = quot; + (-b - Math.sqrt(delta))/ (2.0 * a));
}
else {
System.out.println (“ Single root: quot;);
System.out.println (quot; x = quot; + (-b / (2.0 * a)));
}
21

21. 1
22

22. Start
Input coefficients a,b,c
Computes discriminant
Delta = b * b – 4 * a * c
<0
>0 Discriminant
Sign
=0
Computes roots Computes single root
print roots print root print no roots
End
23

23. & (
Start
Input coefficients a,b,c
Computes discriminant
Delta = b * b – 4 * a * c
<0
>0 Discriminant
Sign
=0
Computes Complex roots
Computes roots Computes double root
print roots print root print roots
End
24

24. delta = (b*b) - (4*a*c); // discrimant computation
if (delta < 0.0) {
System.out.println (quot; No rootsquot;);
}
else if (delta > 0.0) {
System.out.println (quot; Two roots :quot;);
System.out.println (quot; x1 = quot; + (-b + Math.sqrt(delta))/ (2.0 * a));
System.out.println (quot; x2 = quot; + (-b - Math.sqrt(delta))/ (2.0 * a));
}
else {
System.out.println (“ Single root: quot;);
System.out.println (quot; x = quot; + (-b / (2.0 * a)));
}
25

25. quot; quot;
delta = (b*b) - (4*a*c); // discrimant computation
if (delta < 0.0) {
System.out.println (quot; No rootsquot;);
}
else if (delta > 0.0) {
System.out.println (quot; Two roots :quot;);
System.out.println (quot; x1 = quot; + (-b + Math.sqrt(delta))/ (2.0 * a));
System.out.println (quot; x2 = quot; + (-b - Math.sqrt(delta))/ (2.0 * a));
System.out.println (quot; Complex rootsquot;);
System.out.println (quot; x1 real part = quot; + (-b / (2.0*a)));
System.out.println (quot; x2 imaginary part = quot; + (-b - Math.sqrt(-delta))/ (2.0*a)+ quot;iquot;);
System.out.println (quot; x2 real part = quot; + (-b / (2.0*a)));
System.out.println (quot; x2 imaginary part= quot; + (-b - Math.sqrt(-delta))/ (2.0*a)+ quot;iquot;);
}
else {
System.out.println (“ Single root: quot;);
System.out.println (quot; x = quot; + (-b / (2.0 * a)));
}
26

26. 1
27

27. , )& +* ,
y
X1 X2
x
X
X
X
28

28. & +* ,)
Discriminat
Sign
<0
>0
=0
Computes root case 1 Computes roots case 2 2
T F
T F ( /X1/ <= X & X <=
X == X1
/X2/ )
Return True Return False Return True Return False Return False
End
29

29. & * ) quot;(
Initial Request
1 Day
After
1 Week
After
30

30. & * ) quot;(
Initial Request Evolution Request
1 Day
After
Few Weeks Later ?
1 Day
1 Week
After
After
31

31. &
static boolean isInBetweenRoots(double x,double a,double b, double c) {
double delta, x1, x2;
delta = (b*b) - (4*a*c);
if (delta < 0.0)
return false;
else if (delta > 0.0) {
System.out.print(quot;delta > 0quot;);
x1 = (-b + Math.sqrt(delta))/ (2.0*a);
x2 = (-b - Math.sqrt(delta))/ (2.0*a);
return (Math.abs(x1) <= Math.abs(x)) && (Math.abs(x) <= Math.abs(x2));
}
else {
x1 = -b / (2.0 * a);
return (x == x1);
}
}
32

32. 1
33

33. - ) -
6HFRQG 2UGHU
3 RO QRP L D O
6L QJ O H 5 RRW 7 Z R 5 RRW V 1 R 5 RRW
6HFRQG 2UGHU 6HFRQG 2UGHU 6HFRQG 2UGHU
3 RO QRP L D O 3 RO QRP L D O 3 RO QRP L D O
34

34. - ) -
6HFRQG 2UGHU
3 RO QRP L D O ' L V FUL P L QD QW
6L QJ O H 5 RRW 7 Z R 5 RRW V 1 R 5 RRW
6HFRQG 2UGHU 6HFRQG 2UGHU 6HFRQG 2UGHU
3 RO QRP L D O 3 RO QRP L D O 3 RO QRP L D O
35

35. - #
6HFRQG 2UGHU
3 RO QRP L D O
' L V FUL P L QD QW
Double a
Double b
Double c
computeRoots()
6L QJ O H 5 RRW 7 Z R 5 RRW V 1 R 5 RRW
6HFRQG 2UGHU 6HFRQG 2UGHU 6HFRQG 2UGHU
3 RO QRP L D O 3 RO QRP L D O 3 RO QRP L D O
computeRoots() computeRoots() computeRoots()
36

36. - & #
6HFRQG 2UGHU
3 RO QRP L D O
computeRoots()
create()
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6HFRQG 2UGHU 6HFRQG 2UGHU 6HFRQG 2UGHU
3 RO QRP L D O 3 RO QRP L D O 3 RO QRP L D O
computeRoots() computeRoots() computeRoots()
37

37. 1
38

38. -
' L V FUL P L QD QW
6HFRQG 2UGHU
3 RO QRP L D O
39

39. - )
6HFRQG 2UGHU
3 RO QRP L D O
6HFRQG 2UGHU
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' L V FUL P L QD QW
40

40. - )
6HFRQG 2UGHU
3 RO QRP L D O
6HFRQG 2UGHU
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) D FW RU
' L V FUL P L QD QW
41

41. - #
6HFRQG 2UGHU
3 RO QRP L D O
' L V FUL P L QD QW
Double a
Double b
Double c
computeRoots()
6L QJ O H 5 RRW 7 Z R 5 RRW V 1 R 5 RRW
6HFRQG 2UGHU 6HFRQG 2UGHU 6HFRQG 2UGHU
3 RO QRP L D O 3 RO QRP L D O 3 RO QRP L D O
computeRoots() computeRoots() computeRoots()
42

42. class Discriminant {
private double delta;
public Discriminant (double a, double b, double c) {
delta = (b * b) - (4.0 * a * c);
}
public double value () {
return delta;
}
}
43

43. ) *
static Polynome create( double a, double b, double c) {
Discriminant theDiscriminant = new Discriminant(a,b,c);
double delta = theDiscriminant.value();
Polynome polynome;
if (delta == 0.0) {
return polynome = new SingleRootPolynome(a,b,c,theDiscriminant) ;
}
else if (delta > 0.0) {
return polynome = new TwoRootsPolynome(a,b,c,theDiscriminant) ;
}
else {
return polynome = new NoRootPolynome(a,b,c,theDiscriminant);
}
}
44

44. * &
static Polynome create( double a, double b, double c) {
Discriminant theDiscriminant = new Discriminant(a,b,c);
double delta = theDiscriminant.value();
Polynome polynome;
if (delta == 0.0) {
return polynome = new SingleRootPolynome(a,b,c,theDiscriminant) ;
}
else if (delta > 0.0) {
return polynome = new TwoRootsPolynome(a,b,c,theDiscriminant) ;
}
else {
return polynome = new ComplexRootsPolynome(a,b,c,theDiscriminant);
}
}
45

45. 1
46

46. - #
6HFRQG 2UGHU
3 RO QRP L D O
' L V FUL P L QD QW
Double a
Double b
Double c
computeRoots()
6L QJ O H 5 RRW 7 Z R 5 RRW V 1 R 5 RRW
6HFRQG 2UGHU 6HFRQG 2UGHU 6HFRQG 2UGHU
3 RO QRP L D O 3 RO QRP L D O 3 RO QRP L D O
computeRoots() computeRoots() computeRoots()
47

47. & ) *
void computesRoots() {
System.out.println (quot; Single root: quot;);
System.out.println (quot; x = quot; + (-b / (2.0*a)));
}
48

48. - #
6HFRQG 2UGHU
3 RO QRP L D O
' L V FUL P L QD QW
Double a
Double b
Double c
computeRoots()
6L QJ O H 5 RRW 7 Z R 5 RRW V 1 R 5 RRW
6HFRQG 2UGHU 6HFRQG 2UGHU 6HFRQG 2UGHU
3 RO QRP L D O 3 RO QRP L D O 3 RO QRP L D O
computeRoots() computeRoots() computeRoots()
49

49. & ) #*
void computesRoots() {
System.out.println (quot; Two roots :quot;);
System.out.println (quot; x1 = quot; + (-b + Math.sqrt(discriminant.value()))/ (2.0*a));
System.out.println (quot; x2 = quot; + (-b - Math.sqrt(discriminant.value()))/ (2.0*a));
}
50

50. - #
6HFRQG 2UGHU
3 RO QRP L D O
' L V FUL P L QD QW
Double a
Double b
Double c
computeRoots()
6L QJ O H 5 RRW 7 Z R 5 RRW V 1 R 5 RRW
6HFRQG 2UGHU 6HFRQG 2UGHU 6HFRQG 2UGHU
3 RO QRP L D O 3 RO QRP L D O 3 RO QRP L D O
computeRoots() computeRoots() computeRoots()
51

51. & ). *
void computesRoots() {
System.out.println (quot; No rootsquot;);
}
52

52. 1
53

53. - #
6HFRQG 2UGHU
3 RO QRP L D O
' L V FUL P L QD QW
Double a
Double b
Double c
computeRoots()
6L QJ O H 5 RRW 7 Z R 5 RRW V 1 R 5 RRW
6HFRQG 2UGHU 6HFRQG 2UGHU 6HFRQG 2UGHU
3 RO QRP L D O 3 RO QRP L D O 3 RO QRP L D O
computeRoots() computeRoots() computeRoots()
54

54. - #
6HFRQG 2UGHU
3 RO QRP L D O
' L V FUL P L QD QW
Double a
Double b
Double c
computeRoots()
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6HFRQG 2UGHU 6HFRQG 2UGHU 6HFRQG 2UGHU
3 RO QRP L D O 3 RO QRP L D O 3 RO QRP L D O
computeRoots() computeRoots() computeRoots()
55

55. & )& (*
void computesRoots() {
System.out.println (quot; Complex rootsquot;);
System.out.println (quot; x1 real part = quot; + (-b / (2.0*a)));
System.out.println (quot; x1 imaginary part = “
+ (-b + Math.sqrt(-discriminant.value()))/ (2.0*a)+
quot;iquot;);
System.out.println (quot; x2 real part = quot; + (-b / (2.0*a)));
System.out.println (quot; x2 imaginary part = “
+ (-b - Math.sqrt(-discriminant.value()))/ (2.0*a)+
quot;iquot;);
}
56

56. 1
57

57. -
6HFRQG 2UGHU
3 RO QRP L D O
computeRoots()
isInBetweenRoots()
6L QJ O H 5 RRW 7 Z R 5 RRW V 1 R 5 RRW
6HFRQG 2UGHU 6HFRQG 2UGHU 6HFRQG 2UGHU
3 RO QRP L D O 3 RO QRP L D O 3 RO QRP L D O
computeRoots() computeRoots() computeRoots()
isInBetweenRoots() isInBetweenRoots() isInBetweenRoots()
58

58. /+ )
boolean isInBetweenRoots(double x) {
return (x == x1);
}
59

59. -
6HFRQG 2UGHU
3 RO QRP L D O
computeRoots()
isInBetweenRoots()
6L QJ O H 5 RRW 7 Z R 5 RRW V 1 R 5 RRW
6HFRQG 2UGHU 6HFRQG 2UGHU 6HFRQG 2UGHU
3 RO QRP L D O 3 RO QRP L D O 3 RO QRP L D O
computeRoots() computeRoots() computeRoots()
isInBetweenRoots() isInBetweenRoots() isInBetweenRoots()
60

60. /+ )#
boolean isInBetweenRoots(double x) {
return (Math.abs(x1) <= Math.abs(x)) &&
(Math.abs(x) <=
Math.abs(x2));
}
61

61. -
6HFRQG 2UGHU
3 RO QRP L D O
computeRoots()
isInBetweenRoots()
6L QJ O H 5 RRW 7 Z R 5 RRW V 1 R 5 RRW
6HFRQG 2UGHU 6HFRQG 2UGHU 6HFRQG 2UGHU
3 RO QRP L D O 3 RO QRP L D O 3 RO QRP L D O
computeRoots() computeRoots() computeRoots()
isInBetweenRoots() isInBetweenRoots() isInBetweenRoots()
62

62. /+ )
boolean isInBetweenRoots(double x) {
return false;
}
63

63. 01
11
64