Number and Types of Polynomial Roots

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

• positive, 2 or 0 negative

• positive, 1 negative

• 0 positive, 1 negative

• positive, 0 negative

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

A Polynomial of Degree 6 CAN have the following number of imaginary roots:

• 1

• 4

• 3

• 8

What is the name of the polynomial that has 4 roots?

• Quadratic

• Quartic

• Cubic

• Quintic

A polynomial has solutions at x = 2, x = -1, and x = 3. Multiply the factors and choose the correct polynomial.

• x³ - 4x² + x - 6

• x³ - 4x² + x + 6

• x³ + 6x² + x + 6

• x³ - 4x² - x + 7

Which of the following is NOT a factor for the polynomial with roots -2, 3/4, and 5i

• (x + 5i)

• (x + 2)

• (3x - 4)

• (4x - 3)

• 3 real positive, 2 real negative, 0 imaginary

• 0 real positive, 1 real negative, 4 imaginary

• 1 real positive, 2 real negative, 2 imaginary

• 1 real positive, 0 real negative, 4 imaginary

Descartes' Rule of Signs is helpful is solving what kind of equation?

• rational

• exponential

• logarithmic

• polynomial

This is a degree 4 function. Describe the number and types of roots.

• 2 real roots (no repeats)

• 2 real roots ( 1 unique with multiplicity 2), 2 complex roots

• 2 complex roots (no repeats)

• 2 real roots (1 unique with multiplicity 2)

Use the Fundamental Theorem of Algebra to determine the total number of solutions.

• A

• B

• C

• D