Complex Zeros - Algebra - Lecture Notes, Study notes of Algebra

Complex Zeros, Information, Polynomial, Coefficients, Real Coefficients, Remaining Zeros, Function, Polynomial, Product of Linear Factors, Algebra are the key points of this lecture.

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2011/2012

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Lesson
Complex Zeros
Information is
g
iven about a pol
y
nomial f(x) whose coefficients are real numbers. Find the remainin
g
zeros of f.
1) Degree 3; zeros: 3, 1 - i
2) Degree 4; zeros: i, 2 + i
3) Degree 5; zeros: 6, 3 + 5i, -6i
4) Degree 6; zeros: 3, 2 + i, -4 - i, 0
Form a pol
y
nomial f(x) with real coefficients havin
g
the
g
iven de
g
ree and zeros.
5) Degree 3: zeros: 1 + i and -10
6) Degree: 3; zeros: -2 and 3 + i.
7) Degree: 4; zeros: -1, 2, and 1 - 2i.
Use the
g
iven zero to find the remainin
g
zeros of the function.
8) f(x) = x4 - 12x2 - 64; zero: -2i
9) f(x) = x3 - 2x2 - 11x + 52; zero: -4
10) f(x) = x3 + 5x2 + 17x + 13; zero: -2 + 3i
Find all zeros of the function and write the pol
y
nomial as a product of linear factors.
11) f(x) = x3 - x2 + 25x - 25
12) f(x) = x3 + 6x2 + 1x - 34
13) f(x) = x3 + 3x2 + 3x - 7
14) f(x) = x4 + 6x3 + 17x2 + 54x + 72
CollegeAlgebra
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Lesson

Complex Zeros

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining

zeros of f.

1) Degree 3; zeros: 3, 1 - i

2) Degree 4; zeros: i, 2 + i

3) Degree 5; zeros: 6, 3 + 5i, -6i

4) Degree 6; zeros: 3, 2 + i, -4 - i, 0

Form a polynomial f(x) with real coefficients having the given degree and zeros.

5) Degree 3: zeros: 1 + i and -

6) Degree: 3; zeros: -2 and 3 + i.

7) Degree: 4; zeros: -1, 2, and 1 - 2i.

Use the given zero to find the remaining zeros of the function.

8) f(x) = x4 - 12x2 - 64; zero: -2i

9) f(x) = x3 - 2x2 - 11x + 52; zero: -

10) f(x) = x3 + 5x2 + 17x + 13; zero: -2 + 3i

Find all zeros of the function and write the polynomial as a product of linear factors.

11) f(x) = x3 - x2 + 25x - 25

12) f(x) = x3 + 6x2 + 1x - 34

13) f(x) = x3 + 3x2 + 3x - 7

14) f(x) = x4 + 6x3 + 17x2 + 54x + 72

College Algebra

Answer Key

Testname: 16_COMPLEX ZEROS

  1. 1 + i
    • i, 2 - i
  2. 3 - 5i, 6i
  3. 2 - i, - 4 + i
  4. f(x) = x3^ + 8x2^ - 18x + 20
  5. f(x) = x3^ - 4x2^ - 2x + 20
  6. f(x) = x4^ - 3x3^ + 5x2^ - x - 10
  7. 2i, 4, - 4
  8. 3 + 2i, 3 - 2i
    • 2 - 3i, - 1
  9. f(x) = (x - 1)(x + 5i)(x - 5i)
  10. f(x) = (x - 2)(x + 4 + i)(x + 4 - i)
  11. f(x) = (x - 1)(x + 2 + i 3)(x + 2 - i 3)
  12. f(x) = (x + 4)(x + 2)(x - 3i)(x + 3i)

College Algebra