U6 L9 Complex Zeros Lesson.notebook

1

Factoring polynomial functions with complex roots completely using synthetic division and factoring

Finding all real (including complex) zeros of polynomial functions using synthetic division and factoring

U6 L9 Complex Zeros

Read through these notes and try the problems.  I will post a recording of me doing these problems later today 5/18.

Find the zeros. x3+x2+4x = 0

Fundamental Theorem of AlgebraA polynomial function of degree n has n 

complex zeros (real & nonreal).  Some of these zeros may be repeated.

U6 L9 Complex Zeros Day 1

FACTOR out a GCF.

use quad form or CTS.

U6 L9 Complex Zeros Lesson.notebook

2

If 3+√2 is a zero, then _______ is also a zero.

IF 3i is a zero, then ______ is also a zero.

If 7-3i is a complex zero, then _______ is also a zero.

Complex Conjugate ZerosIf a+bi is a zero of a Polynomial Function, then its complex conjugate a­bi is also a zero.

same is true for real conjugates

b) g(x) = (x-5)(x-√2 i)(x+√2 i)a)

no x­intercepts

x­intecept

U6 L9 Complex Zeros Lesson.notebook

3

Write a polynomial of minimum degree in standard form with real coefficients whose zeros include: 2, -3 and 2i.

Write a polynomial of minimum degree in standard form with real coefficients whose zeros include: 2+3i

Finish this one!!

U6 L9 Complex Zeros Lesson.notebook

4

Write a polynomial of minimum degree in standard form with real coefficients whose zeros include: 4, -3, and 2 + 5i.