1 / 11

Notes Day 6.2

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

chace
Télécharger la présentation

Notes Day 6.2

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Notes Day 6.2 Irrational Root Theorem Imaginary Root Theorem Factors and their multiplicity Find relative max/min on the graphing calculator

  2. 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 _________________

  3. Write a quartic Polynomial equation that has zeros at 1, -1, and

  4. 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 _____________________

  5. Write a cubic Polynomial equation that has zeros at 2 and 4+i ix -4x x2 -8x2 17x x3 -4x 16 -4i -ix 4i -2x2 16x -i2 -34

  6. 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

  7. Solve the equation! The square root method works since no linear term x2+ 4 = 0 x2 = – 4

  8. Solve the equation!

  9. Solve the equation!

  10. Factor to find roots but use calculator to find relative min/max. y = 2x3 + 14x2 – 3x – 21 y-int = -21

  11. Factor to find roots but use calculator to find relative min/max. y = 3x5 + 18x4 + 27x3 Work this on back of your notes! Local minimum is: -25

More Related