Take_home_Q5

Take_home_Q5 - Students Name: Signature: Quiz 5: Section...

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Student’s Name: Signature: 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 non-zero imaginary part (i.e., a complex (NOT REAL) number)? For the complex (NOT REAL) zeros, you know that they have to appear in CONJU-
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Take_home_Q5 - Students Name: Signature: Quiz 5: Section...

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