0 Wed 12/2 Lesson 5 – 5 Learning Objective: To apply Rational Root Thm (& Descartes’Rule) Hw: W.S. 5-5.

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Wed 12/2 Lesson 5 – 5 Learning Objective: To apply Rational Root Thm (& Descartes’Rule) Hw: W.S. 5-5

Algebra II

 To understand & apply the Rational Root Theorem  To understand & apply the Conjugate Root Theorem  (To understand and apply Descartes’ Rule of Signs)

Look at COEFFICIENTS

q = 1 p = 12

q = 3 p = 10 Divide each numerator by each denominator

q = 1 p = 42

Step 2: Test each possible rational root in original function until you find a root.  Do synthetic substitution until get R0

1 Nope! 1 is NOT a root! Try something else!

2 YES! 2 IS a root!

q = 2 p = 6

YES! -1 IS a root!

2 Sign Change 1 Sign Change  Sum = 3

5 Sign Change 4 Sign Change

 It could have 5 positive roots, 4 negative roots, & 0 imaginary roots  It could have 3 positive roots, 2 negative roots, & 4 imaginary roots

3 Sign Change 1 Sign Change It could have 3 + roots, 1 - root, & 0 imaginary roots It could have 1 + roots, 1 - root, & 2 imaginary roots

q = 1 p = 6

1 YES! 1 IS a root!