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Quiz 5: Section 3.6
1
Reminder of the complex zeros
•
If
z
=
a
+
bi
is a complex (NOT REAL) zero of the polynomial
f
(
x
), then its conjugate
z
=
a

bi
is also a complex zero of
f
.
In other words, the complex zeros occur as
CONJUGATE pairs.
•
If
f
is a polynomial of degree
n
, then it can be factored into
n
LINEAR factors (if
complex numbers are allowed in the linear factors).
Hence,
f
will have
n
complex
zeros.
•
If
f
is a polynomial of ODD degree
n
, then
f
has
at least one
REAL zero. Why?
Because complex zeros occur as conjugate pairs, there will be EVEN numbers of zeros
that are NOT real numbers. Consequently, since
f
has
n
zeros (
n
ODD), one of its
zeros has to be a REAL number.
2
Question 1 (5 points)
This is the Example 1 in the lecture notes of Section 3.6.
Hints:
•
What is the given degree of the polynomial
f
? Then how many zeros does
f
have?
Look at the given zeros, which one is a real number, and which one is a complex
number with nonzero imaginary part (i.e., a complex (NOT REAL) number)?
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 Spring '11
 Nuegyen
 Complex number, −

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