Descartes' Rule of Rational Root Theorem and Finding All Zeros

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

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

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

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

Find the zeros of the polynomial given one factor. Use synthetic division.

• X= 3,4,5

• x=-3,-4,-5

• x=-3,4,5

• x= 3, -4, -5

Find all zeros. Do not use the calculator.

• x= 3,1,1/3

• x= -3, -1, -1/3

• x = -3, 1, 1/3

• x = 3, -1, -1/3

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

Write a polynomial function with rational coefficients that has zeros - 4 and 5i.

• P(x) = x³ + 4x² + 25x + 100

• P(x) = 5x³ - 4x² + 25x + 100

• P(x) = x³ + x² - 25x + 100

• P(x) = 4x² + 5