Sharp PC-1500 Applications Manual page 26

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PROG RAM
TIT LE
'
QUADRAT IC A ND CUBIC EQUAT IONS
(2) When
q
2 +
4p
3
<
0, u
3
and v
3
arc imaginary roots.
Let u
3
=
rcie
then v
3
=
re-
10,
r
=
_ p3
J-ql - 4pJ
8 = tan
1
therefore,
-q
,.--,.,...( 9 . . 9 )
1 i =J
1·
c-os3 -
ls1n3
" - r=JT"(c·o•
~
·
i
• in
~ )
Through this, roots a ,
/3
and 'Y
of
Y
3
+
3PY
+
q
=
0
arc as follows:« =
-2.[T,
in
(..'.:.-~)
2 3
::' f)
/J = - 2J-f'
s i"
(6 1" 3 )
~
c .::. __
o l
·y =- 2 J
- r s i n
6 3
This is t he case o f three differen t real roots.
PROG RAM NO.
PS- A- 6
(3)
When
p
1
+4 p
3
= O
and
p '\ 0,
u
3
=
v
3
= -
i
is obtained.
Therefore, from U
=
V
=
V -
i
°'
=
2 u
f3='Y= - u
This is the case of
a
double root and a another root.
(4 ) If
q
2 + 4p 3
= O and
p
= 0,
q
=
0 is obtained. Therefore,
since u =
v
=
0,
t he result is;
a=f3 = ' Y = 0
This is
a
triple root.
Adding
~
to
°' •
{3
and 'Y
finds solutions to the equation .
Be noted that when 2 or 3 different roots arc very close to each other, they
may
be regarded as a
double
or triple root and
vice versa.
I
Printout
I
REAL
5 . 403B82032E- 01
REAL
- 3 . 903882032£- 01
* **REAL***
- 0 .
4
IM AGIN ARY
0.2
REAL ROOT
1 . 4 14213562
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