Civil Engineering Reference
In-Depth Information
This can be written with the coefficients in a vertical format as follows:
2
a
2
3
a
aa
a
2
2
a
−
+
−
2
2
2
aa
aa
a
n
1
n
−
1
n
−
2
24
n
−
3
0
=+
−
y
y
+−
+
2
2
y
+
y
13
2
a
2
15
4
6
2
a
aa
aa
aa
4
−
+
−
2
2
2
35
+
y
n
−
4
++
a
2
26
n
17
+
2
a
8
A tabular solution may be set up considering the following general
polynomial:
n
n
−
1
n
−
2
n
−
3
1
fx ax ax ax
()=
+
+
+ ++ +=
ax
ax a
0
0
1
2
3
n
−
1
n
Carefully inspect the coefficient of the polynomial for a pattern. The solu-
tion of the original polynomial can take three different forms. These are
shown in Figure 1.11.
• Real and distinct roots
• Real and equal roots
• Complex roots
f(x)
f(x)
f(x)
(x)
(x)
(x)
One real and
one imaginary root
One real and
one double root
Three real roots
Figure 1.11.
Graeffe's root squaring method
.
