Civil Engineering Reference
In-Depth Information
The Enke root relationship is then as follows:
b
=++
=
r
mmm
r
r
1
1
2
3
mm mm mm
brr
+
r r
+
r r
2
1
2
1
3
2
3
b rrr
=
mmm
3
1 23
If we consider only the dominant terms in each expression, the following
occurs:
br
brr
b rrr
≅
≅
≅
m
1
1
mm
2
1
2
mmm
3
1 23
These become the following:
1
brrb
≅∴≅
m
m
1
1
1
1
1
≅ ∴≅≅∴=
b
r
b
b
b
b
m
mm m
brr
r
2
2
r
2
2
1
2
2
2
m
1
1
1
1
∴≅ ≅∴=
b
rr
b
b
b
b
m
mmm m
3
3
3
br
≅
1123
rr r
r
3
3
3
mm
12
2
2
The general expression for this regular solution is the following:
1
≅∴=
b
b
b
b
m
m
n
n
r
r
n
n
n
−
1
n
−
1
The Enke roots only lack the proper sign and either positive or negative
may be correct, so a check is necessary.
Example 1.14 Graeffe's root squaring method—real and distinct
roots.
Find the root of the following polynomial using Graeffe's root squaring
method.
fx
()==−+−+
0
x
4
1050 4
x
3
x
2
x
