Graphics Programs Reference
In-Depth Information
Thanks to the good starting value, this approximationis already quite close to the
exact value
r
=
3
.
20
−
0
.
80
i
.
EXAMPLE 4.12
Use
polyRoots
to compute
all
the roots of
x
4
−
5
x
3
−
9
x
2
+
155
x
−
250
=
0.
Solution
The command
>> polyroots([1 -5 -9 155 -250])
results in
ans =
2.0000
4.0000 - 3.0000i
4.0000 + 3.0000i
-5.0000
There aretwo real roots (
x
=
2 and
−
5) and a pair of complex conjugate roots
(
x
=
4
±
3
i
).
PROBLEM SET 4.2
Problems 1-5
A zero
x
r
of
P
n
(
x
) is given. Verify that
r
is indeedazero, and then
deflate the polynomial, i.e., find
P
n
−
1
(
x
)sothat
P
n
(
x
)
=
=
(
x
−
r
)
P
n
−
1
(
x
)
.
=
3
x
3
+
7
x
2
−
+
=−
.
1.
P
3
(
x
)
36
x
20,
r
5
2.
P
4
(
x
)
=
x
4
−
3
x
2
+
3
x
−
1,
r
=
1
.
x
5
30
x
4
361
x
3
2178
x
2
3.
P
5
(
x
)
=
−
+
−
+
6588
x
−
7992,
r
=
6
.
x
4
5
x
3
2
x
2
4.
P
4
(
x
)
=
−
−
−
20
x
−
24,
r
=
2
i
.
3
x
3
19
x
2
5.
P
3
(
x
)
=
−
+
45
x
−
13,
r
=
3
−
2
i
.
Problems 6-9
A zero
x
r
of
P
n
(
x
) is given. Determine all the other zeroes of
P
n
(
x
)
by using a calculator. You shouldneedno tools other than deflation and the quadratic
formula.
6.
P
3
(
x
)
=
x
3
8
x
2
=
+
1
.
−
9
.
01
x
−
13
.
398,
r
=−
3
.
3
.
x
3
64
x
2
7.
P
3
(
x
)
=
−
6
.
+
16
.
84
x
−
8
.
32,
r
=
0
.
64
.
2
x
3
13
x
2
8.
P
3
(
x
)
=
−
+
32
x
−
13,
r
=
3
−
2
i
.
x
4
3
x
3
10
x
2
9.
P
4
(
x
)
=
−
+
−
6
x
−
20,
r
=
1
+
3
i
.
Problems 10-16
Find all the zeroes of the given
P
n
(
x
).
10.
x
4
1
x
3
52
x
2
P
4
(
x
)
=
+
2
.
−
2
.
+
2
.
1
x
−
3
.
52
.
x
5
156
x
4
5
x
3
780
x
2
11.
P
5
(
x
)
=
−
−
+
+
4
x
−
624
.
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