Civil Engineering Reference
In-Depth Information
=
±
()
−
()
=±=−
2
1
1 46
2
(
)
2
xx with x
−−
16
05 25 23
.
.
,
12
,
The first two roots are
x
3
=
−
2 and
x
4
=
3
.
The remaining values are the
coefficients of the factored polynomial.
(
)
−−
(
)
(
)
2
2
22 16 4
fx x
()=++
x xx x
−
The last root is
x
5
=
4, which is the value in the remaining polynomial of
degree one
x − r = x −
4
.
The final factored form of the original quadratic
can be written and the five roots are
x
1
= −
1
+i
,
x
2
= −
1
−i
,
x
3
= −
2,
x
4
=
3,
and
x
5
=
4
.
(
)
(
)
(
)
(
)
2
22 2
fx x
()=++
x
x
+
x
−
3
x
−
4
REfEREncES
Bairstow, L. 1920.
Applied Aerodynamics.
London, England: Longmans, Green
and Co.
Descartes, R. 1637.
Discours de la méthode pour bien conduire sa raison, et
chercher la vérité dans les sciences
. Lieden, Netherlands.
James, M.L., G.M. Smith, and J.C. Wolford. 1977.
Applied Numerical Methods
for Digital Computations
.
2nd ed. Boston, Massachusetts: Addison-Wesley
Longman Publishing Co., Inc.
Newton, I. 1669.
De analysi per aequationes numero terminorum infinitas,
,
London, England.
Taylor, B. 1715.
Methodus Incrementorum Directa et Inversa
. London, England.
