THE FUNDAMENTAL THEOREM OF ALGEBRA

Réussis tes devoirs et examens dès maintenant avec Quizwiz!

Based on the Fundamental Theorem of Algebra, how many complex roots does each of the following equations have? Write your answer as a number in the space provided. For example, if there are twelve complex roots, type 12. x(x2 - 4)(x2 + 16) = 0 has a0 complex roots (x 2 + 4)(x + 5)2 = 0 has a1 complex roots x6 - 4x5 - 24x2 + 10x - 3 = 0 has a2 complex roots x7 + 128 = 0 has a3 complex roots (x3 + 9)(x2 - 4) = 0 has a4 complex roots

2, 4, 6, 7, 5

A polynomial equation has only imaginary roots and no real root. Which options CANNOT be the degree of that polynomial? (Select all that apply.)

3, 7

What is the least possible degree of a polynomial that has the root -3 + 2i, and a repeated root -2 that occurs twice?

4

What is the least possible degree of a polynomial that has roots -5, 1 + 4i, and -4i?

5

Solve the following equation by identifying all of its roots including any imaginary numbers and multiple roots. (x2 - 1)(x2 + 2)(x + 3)(x - 4)(x + 1) = 0

x = 4 x = -3 x= 0.0000 - 1.4142 i x= 0.0000 + 1.4142 i x = 1 x = -1

Which of these polynomial equations is of least degree and has -1, 2, and 4 as three of its roots?

x3 - 5x2 + 2x + 8 = 0

Solve for the roots in the equation below. x4 + 3x2 - 4 = 0

x= -1, 1, 2i. -2i

Solve the following equation by identifying all of its roots including all real and complex numbers. In your final answer, include the necessary steps and calculations. Hint: Use your knowledge of factoring polynomials. (x2 + 1)(x3 + 2x)(x2 - 64) = 0

x^5+2x^3)(x^3+2x)(x^5-64x^3)(2x^3-128x) x= i, -i, 0, i square root 2, i square root -2, 8, -8

Write a polynomial equation of degree 3 such that two of its roots are 2 and an imaginary number.

y = (x - 2)(x - i)(x + i)

Solve for the roots of x in each of the equations below. x4 - 81 = 0 x4 + 10x2 + 25 = 0 x4 - x2 - 6 = 0

A) x^4-81=0 - x= 3, -3 B) x^4+10x^2+25=0 - x= i square root 5, i square root -5 C) x^4- x^2-6=0 - x= square root 3, square root -3, i square root 2, -i square root 2

Which polynomial equations have -i as one of their roots?

x3 + 3x2 + x + 3 = 0 x3 - 6x2 - 16x + 96 = 0

Which polynomial equation of least degree has -2, -2, 3, and 3 as four of its roots?

(x + 2)2(x - 3)2 = 0

Solve for the roots in the equation below. In your final answer, include each of the necessary steps and calculations. Hint: Use your knowledge of polynomial division and the quadratic formula. x3 - 27 = 0

(x+3)(x^2-3x+9)=0

Find all the roots of the equation x4 - 2x3 + 14x2 - 18x + 45 = 0 given that 1 + 2i is one of its roots.

1+3=5x3, 5xp, =3 roots because of all of its roots divid

A. How many real roots does the function have? B. Complete the equation of the graphed function. y= (x - )(x + )2

2, 2, 4

Which is a possible number of distinct real roots for a cubic function? Select all that apply.

2, 3, 0

How many roots does the equation -2x3 = 0 have?

3


Ensembles d'études connexes

Cardiovascular Disorders Passpoint

View Set

EMU IT150/IA150 Networking -- Bemus Final

View Set

Chapter 12: The Supply of and Demand for Productive Resources

View Set

Microbiology by Bauman Chapter 9 Q & A

View Set

2.8 Inserting, updating, and deleting rows

View Set

Leadership and Change Chapters 5 & 6

View Set

Chapter 12 Oncologic Disorders Prep U

View Set

Chapter 4: Ancient India and China

View Set

questions for laws of Thermodynamics

View Set

PrepU Ch 37: Management of Patients with Musculoskeletal Trauma

View Set