Rational Root Theorem and Descartes

Use Descartes Rule of Signs to determine the possible number of positive and negative roots.

• positive, 2 or 0 negative

• positive, negative

• 0 positive, negative

• What?

How many possible negative rational solutions answers are there for x⁴ - 17x³ + 77x² - 127x + 66 = 0?

(a)  

What does the Descarte's Rule of Signs tell you?

• The quantity of possible positive & negative solutions

• The possible rational solutions

• How many total solutions

• The prime factorization

Use Descartes Rule of Signs to determine the possible number of positive and negative roots.

• 3 or 1 positive roots and 0 negative roots

• 4, 2, or 0 positive roots and 1 negative root

• 4, 2, or 0 positive roots and 0 negative roots

• What?

• Fundamental Theorem of Algebra

• Rational Root Theorem

• Descartes' Rule of Signs

• End Behavior Rules

• Fundamental Theorem of Algebra

• Rational Root Theorem

• Descartes' Rule of Signs

• End Behavior Rules

• There are only roots that are fractions.

• There are only roots that are integers.

• There are only complex roots.

• There are only positive roots.

What are all the possible rational roots of x³ - 4x² + 5x - 12?

• ±1, ±2, ±3, ±4, ±6, ±12

• ±1, ±2, ±3, ±4, ±6

• ±2, ±3, ±4, ±6, ±12

• ±1, ±2, ±4, ±6, ±12

According to the Rational Root Theorem, what are the all possible rational roots? 
x³ - 7x - 6 = 0

• ±1, ±2, ±3

• ±1, ±7

• ±1, ±2, ±3, ±6

• ±1, ±2, ±3, ±6, ±7

List the possible rational zeros of the function: f(x) = 2x³ + 5x - 8

• ±1,±2,±3,±4,±8

• ±1/2, ±1, ±2, ±4

• ±1/2, ±1, ±2, ±4, ±8

• ±1/4, ±1/2, ±1, ±2, ±4, ±8

Tags

CCSS.HSA.APR.B.2