Download Presentation
Notes Day 6.2

Loading in 2 Seconds...

1 / 11

# Notes Day 6.2 - PowerPoint PPT Presentation

Notes Day 6.2. Irrational Root Theorem Imaginary Root Theorem Factors and their multiplicity Find relative max/min on the graphing calculator. Notes 6.2 Irrational Root Theorem. If is an S / R / Z / x-intercept, then the conjugate

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

## PowerPoint Slideshow about 'Notes Day 6.2' - chace

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Notes Day 6.2

Irrational Root Theorem

Imaginary Root Theorem

Factors and their multiplicity

Find relative max/min on the

graphing calculator

Notes 6.2 Irrational Root Theorem

If is an S / R / Z / x-intercept, then the conjugate

__________ must ALSO be an S / R / Z / x-intercept

EXAMPLE

A polynomial equation with integer coefficients has 4 roots.

If two of them are and , what are the other two?

__________________ and _________________

Imaginary Root Theorem

If a + bi is an S / R / Z / x-intercept, then the conjugate

__________ must ALSO be an S / R / Z / x-intercept

EXAMPLE

A polynomial equation with integer coefficients has 4 roots.

If two of them are 3 – i and 2i , what are the other two?

______________________ and _____________________

ix

-4x

x2

-8x2

17x

x3

-4x

16

-4i

-ix

4i

-2x2

16x

-i2

-34

Multiplicity

The number of times an S / R / Z / x-intercept is

___________________ in a given polynomial equation.

REPEATED

EXAMPLES: name the root(s) and multiplicity

y = x(x2 – 4x + 4)

y = x(x-2)(x-2)

Once

2

Once

-1

0

Once

2

Twice

Twice

-4

Solve the equation!

The square root method works since no linear term

x2+ 4 = 0

x2 = – 4

y = 2x3 + 14x2 – 3x – 21

y-int =

-21

y = 3x5 + 18x4 + 27x3

Work this on back of your notes!

Local minimum is:

-25