Number and Types of Roots

Which of these equations has two real roots?

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

• 1 positive, 2 or 0 negative

• 1 positive, 1 negative

• 0 positive, 1 negative

• 1 positive, 0 negative

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

• 2 or 0 positive roots and 1 negative roots

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

• ±1, ±8

• ±1, ±2, ±4, ±8

• ±1, ±2, ±4

• 1, 2, 4, 8

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

• ±1, ±7, ±1/3, ±7/3

• ±1, 7

• ±1, ±3, ±7, ±7/3

• ±1, ±3, ±7, ±1/3, ±7/3

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = 2x³ + 5x² - 9x + 5

• ±1, ±5, ±1/2, ±5/2

• ±1, ±2, ±5, ±1/2, ±5/2

• ±1, ±5

• ±1, ±2, ±5, ±1/2, ±5/2, ±2/5

According to the Rational Root Theorem, what are the all possible rational roots? 
2x³ - 11x² + 12x + 9 = 0

• ±1,±2

• ±1,±3,±9

• ±1,±3±9,±1/2,±3/2,±9/2

• ±1,±2,±1/3,±2/3,±1/9,±2/9

How many positive solutions does the following polynomial have?

f(x) =3x⁵ - x⁴ + 3x² - 6x +11

• 4, 2, or 0

• 4

• 3 or 1

• 3

How many possible negatives solutions does the following polynomial have? f(x) = x⁴ - 3x³ - 17x² + 39x -20

• 3 or 1

• 3

• 1

• 2 or 0

Using Descartes' Rule of Signs, how many possible NEGATIVE roots are there for the polynomial f(x) = x⁴+x³+x²+x+5. Select all that apply.

• 0

• 1

• 2

• 3

• 4