1 / 11

Rational Root Theorem

Rational Root Theorem. No craziness here! We’re all rational . Skeeter Parker Berrien High School Fall 2013. Rational Root Theorem: The Basics. Start by making certain the equation is in descending order and set = 0.

lou
Download Presentation

Rational Root Theorem

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. Rational Root Theorem No craziness here! We’re all rational. Skeeter Parker Berrien High School Fall 2013

  2. Rational Root Theorem: The Basics • Start by making certain the equation is in descending order and set = 0. • The degree of the equation tells you the MOST number of roots you can have. (e.g.: 4th degree can have no more than 4 roots)

  3. The Basics (continued) • There may be less roots if multiplicity is involved. Multiplicity means an individual root actually works more than once. • Multiplicity occurs with perfect square trinomials (among others).

  4. The List of Possibles • Start by making your list of possible roots. Do this by taking ALL factors (+ and − ) of the last term and placing them over ALL factors of the first coefficient. • Put the positives on one row and the negatives on another. This will make things easier later.

  5. Using the List of Possibles • Use synthetic division to find a root. A number is a root if the remainder is zero. This trial and error may take a while. • Once you find a root, reduce the equation. Revisit your list of possible roots, and mark out those which are no longer possible.

  6. Reducing the Equation • Reduce the equation each time you find another root. The goal is to get to a quadratic equation. • Some websites will tell you to keep using the original equation, but this will not help you when you have to find imaginary or irrational roots.

  7. What are you finding? • Read the instructions! They may ask for: • Rational roots only • Real roots only • All roots

  8. Finding Rational Roots Only • If you are asked only to find the RATIONAL roots, you are finished when you have exhausted the list of possibles. • No radicals or imaginaries!

  9. Finding Real Roots Only • If asked to find the REAL roots, you are finished if the quadratic formula yields a negative number under the radical. • May include radicals! • No imaginaries!

  10. Finding All Roots • Finding ALL roots means you have found root after root, reducing the equation along the way until you get a quadratic equation that either gets factored or completely solved by the use of quadratic formula.

  11. Our Goal • Once you get to a quadratic you can either factor or use quadratic formula to find the remaining two roots. • After you have found all roots, put them all in a solution set.

More Related