Roots and Fundamental Theorem of Algebra

Which of the following roots match the above polynomial:

• -3,-1,4

• -3,2i,-2i

What is the total number of roots for the following equation?
y = 4x⁶ - 12x⁵ - x⁴ + 2x³ - 6x² - 5x + 10

• 4

• 5

• 6

• 7

State how many of each type of possible solution the following polynomial has f(x) = -4x⁴ + x³ +11x² - 4x + 8

• Positive: 3 or 1

  Negative: 1

• Positive: 3

  Negative: 1

• Positive: 1

  Negative: 3 or 1

• Positive: 1

  Negative: 3

How many solutions does the polynomial f(x)=3x⁴ + 5x² - 6x have?

• 4

• 2

• 3

• 5

The nth degree of a polynomial is equal to the number of root that same polynomial has: is a true statement of which theorem?

• Factor Theorem

• Remainder Theorem

• Fundamental Theorem

• All of the above

• None of the above

What is the total number of possible negative roots for the following equation? y = 4x⁶ - 12x⁵ - x⁴ + 2x³ - 6x² - 5x + 10

• 4

• 3

• 2

• 5

How many positive solutions does the following polynomial have?

• 4, 2, or 0

• 4

• 3 or 1

• 3

Write a cubic polynomial in standard form with roots 3 and 4i

• x³-3x²+16x-48

• x³-8x²-3x+52

• x³+3x²+3x+1

• x³+3x²-16x+48

State the zeros of the polynomial (include multiplicity):
f(x) = (x²+9)(x -1)³(2x + 5)

• -9, 1, -5

• -9, 1 (multiplicity of 3), -5

• ± 3i , 1 (multiplicity of 3), -5∕2

• ± 3i, 1, -5

Which statement is the Fundamental Theorem of Algebra?

• There are infinitely many rationals between two reals.

• Every polynomial equation having complex coefficents and degree greater than the number 1 has at least one complex root.

• There are infinitely many prime numbers.

• All numbers are rational numbers.