Number and Types of Polynomial Roots

How many roots does the following function have?

f(x)= x⁵ - 3x³ + x

• 8

• 9

• 5

• 3

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

What type of roots does the polynomial have?

• Three real

• One real, and two imaginary

• Two real, and one imaginary

• Three imaginary

• 2

• 3

• 5

• 1

If you know 3 and 2i are roots of a polynomial function, state the polynomial factors.

• (x + 3) , (x + 2i)

• (x - 3), (x -2i), (x + 2i)

• (x - 3), (x + 3), (x - 2i), (x + 2i)

• (x -3 - 2i), (x + 3 - 2i)

How many roots or zeros does the equation
f(x) = 5x⁴-8x³+4x²-6x+3 have?

• 3

• 4

• 5

• 0

How many roots does the polynomial function have?

• 1

• 2

• 3

• 4

The degree of the polynomial determines the number of roots.

• True

• False