U3L8 Rational Root Theorem.notebook -...
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U3L8 Rational Root Theorem.notebook November 07, 2014 Aim: The rational root theorem. Do Now: 1) What is your definition of rational numbers? 2) Create a list of rational numbers. Try to include as many different looking examples as possible. 3) Create a list of irrational numbers. Again, try to include as many different looking examples as possible.
Transcript of U3L8 Rational Root Theorem.notebook -...
U3L8 Rational Root Theorem.notebook November 07, 2014
Aim: The rational root theorem.Do Now:
1) What is your definition of rational numbers?2) Create a list of rational numbers. Try to include as many different looking examples as possible.
3) Create a list of irrational numbers. Again, try to include as many different looking examples as possible.
U3L8 Rational Root Theorem.notebook November 07, 2014
Take 60 seconds to discuss strategies for solving the two problems
Solve for the roots of x2 2x 24
Solve for the roots of x3 2x 24
U3L8 Rational Root Theorem.notebook November 07, 2014
Storytime: Solving Polynomials in the 16th Century
Cardano, Tartaglia and Ferrari
A Story of Scumbaggery
VS
U3L8 Rational Root Theorem.notebook November 07, 2014
Solutions for a quadratic equation
U3L8 Rational Root Theorem.notebook November 07, 2014
Solutions for the general cubic P(x) = ax3 + bx2 + cx + d
U3L8 Rational Root Theorem.notebook November 07, 2014
The solutions for the general quartic polynomial is so large and unwieldy, I cannot fit it legibly onto this screen. (Serious)
U3L8 Rational Root Theorem.notebook November 07, 2014
Goal: Find a way to solve for the roots of cubic and quartic equations without resorting to unmemorizable formulas.
We will introduce a new tool: The Rational Root Theorem
In short: The rational zeros of a polynomial (if they exist) must be a value that is
factors of the last
factors of the first
U3L8 Rational Root Theorem.notebook November 07, 2014
List all the possible rational roots, if they exist, of this polynomial
4x7 + 7x3 + 10,000x 10
Step 1: Factors of the last term: _______________Step 2: Factors of the lead coefficient: _______________Step 3: Create the fractions, put "plus or minus" sign for each
Step 4: Cross out any repeats. This is your entire list of possible rational roots. If a rational root exists, it MUST be one of these.
U3L8 Rational Root Theorem.notebook November 07, 2014
Why is this useful? Is it awesome?
Of all the infinite numbers that could be rational zeroes of a polynomial, this theorem reduces the possibilities (if they exist) to just a small handful.
U3L8 Rational Root Theorem.notebook November 07, 2014
Youtube: Derek owens rational zero
He has 8 videos on this topic. Watch Part 5.
Follow along carefully, write his examples into your notes
What is the difference between what we've been doing so far, and this new problem?
If you need MORE examples, watch parts any of parts 6, 7 or 8!
U3L8 Rational Root Theorem.notebook November 07, 2014
Questions to solve.
Pepper Chap2 PDF (not the hardcopy): Page 357:: #12, 23, 41Supreme Challenge: 49, 58
Solutions for 12, 23, 58 are on Pepper Solutions PDF. These are not complete solutions but are there to steer you in the correct direction.
Reminder: Wolfram can list all the solutions for any polynomial. Use it to check your answer for all questions.
U3L8 Rational Root Theorem.notebook November 07, 2014
End of new material for Unit 3
