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b
= a
(4a
0
0
2
Let y
be the largest real root of the above cubic. Then the fourth–order polynomial
0
is reduced to two quadratic polynomials:
where J = a
3
K = y
/2
0
2
−
J
a
L =
2
K −
2
M =
Roots of the fourth degree polynomial are found by solving these two quadratic
polynomials.
A quadratic equation x
If the discriminant d = (a
complex, being
File name 33s-E-Manual-1008-Publication(1st).doc
Printed Date : 2003/10/8
2
2
– a
) – a
.
3
1
2
x
+ (J + L)x + (K + M) = 0
2
x
+ (J – L)x + (K – M) = 0
/2
+
y
× (the sign of JK – a
0
a
0
2
+ a
x + a
1
0
=
−
x
1
2 ,
2
/2)
– a
1
o
±
=
−
±
u
iv
(
a
) 2
1
Size : 13.7 x 21.2 cm
/2)
1
= 0 is solved by the formula
a
a
±
−
1
(
1
)
a
2
0
2
2
≥ 0, the roots are real; if d < 0, the roots are
−
i
d
.
Mathematics Programs
Page : 386
15–21
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