# what does it mean when two of the zeros of a polynomial function are complex conjugates?

18,761 results

1. ### algebra two

what does it mean when two of the zeros of a polynomial function are complex conjugates?
2. ### HELP!!!!!! ASAP

what does it mean when two of the zeros of a polynomial function are complex conjugates?
3. ### Calculus

Score for Question 2: ___ of 40 points) For the polynomial (x)=x^5-5x^4+12x^3-24x^2+32x-16 , answer the following questions. Show all of your work. How many zeros does the function have over the set of complex numbers? What is the maximum number of local extrema (maxima or ...
4. ### HELP!!!!!! ASAP

which function below if either has zeros that are complex conjugates? P(x)=x^4-7x^3-27x^2+63x+81 H(x)=x^4-x^2+25x-25
5. ### algebra two

which function below, if either, has zeros that are complex conjugates? P(x)= X^4-7x^3-27x^2+63x+81 H(x)=x^3-x^2+25x-25
6. ### functions

a) find the zeros of t(x) =2x^2 + ix + 3. b) The zeros are not complex conjugates. Explain why this does not contradict with the Conjugate Zeros Theorem
7. ### Algebra

I need help with a few questions, please explain. 1. Write a polynomial function in standard form with zeros -1, -1, 6. 2. Find the roots of the equation x^3 – 3x^2 + x + 5 3. Describe the number and type of roots for the polynomial (how many real and complex?). x^3 + 5x^2...
8. ### Find the complex zeros

Find the complex zeros of the polynomial function. Write f in the factored form. f(x)=x^3-3x^2+7x-5 f(x)=
9. ### Algebra

Can someone please explain how to do these problems. 1)write a polynomial function of least degree with intregal coefficients whose zeros include 4 and 2i. 2)list all of the possible rational zeros of f(x)= 3x^3-2x^2+7x+6. 3)Find all of the rational zeros of f(x)= 4x^3-3x^2-...
10. ### Math

Find all complex zeros for the following polynomial function. Please show all of your work. f(x) = x^4 - 91x^2 - 900 Hi, I need help... I'm not understanding this complex zero..
11. ### pre-calculus

find the complex zeros of the polynomial function. write F in the factored form. f(X)=x^3-7x^2+20x-24 use the complex zeros to write f in factored form. f(x)= (reduce fractions and simplify roots)
12. ### algebra

Find the complex zeros of the polynomial function. Write f in factored form. F(x)=x^3-8x^2+29x-52 Use the complex zeros to write f in factored form F(x)=____(reduce fractions and simplify roots)
13. ### Precalculus

There is at least one polynomial with real functions with 9+i as its only nonreal zero. A. The statement is​ false, because the Fundamental Theorem of Algebra dictates that there must be n complex zeros for a polynomial of degree n.   B.The statement is true. If 9 plus ...
14. ### college algebra

find the complex zeros of the polynomial function. write f in factored form. use complex zeros to write f in factored form f(x)= x^3-6x^2+21x-26
15. ### Polynomial Function

Could you please check my answers? Find an nth degree polynomial function with real coefficients satisfying the given conditions. 1. n=3; 3 and i are zeros; f(2)=20 -I got: f(x)=-4^3+12x^2-4x+12 3.n=3;4 and i zeros;f(-3)=60 -I got:f(x)=6x^3+24x^2+6x+24
16. ### Algebra II

Find the complex zeros of the polynomial function: x4+5x2+4
17. ### Algebra II

Write the simplest polynomial function with the zeros 2-i, square root of 5, and -2. I know that the conjugates are 2+i and -the square root of five, but when I multiply it comes out wrong. not sure A toy rocket is launched from the ground level with an initial vertical ...
18. ### calculus

Find the complex zeros of the polynomial function. F(x)=5x^4-16x^3-22x^2+200x-39
19. ### algebra

find all complex zeros for the following polynomial function please show all your work f(x) = x^3 - 125 ????????
20. ### math

find complex zeros of the polynomial function. put f in factored form. f(x)=x^3-6x^2+21x-26
21. ### math

Find the complex zeros of the polynomial function, and write f in factored form: f(x)= x^3 - 8x^2 + 30x - 36
22. ### Algebra

Find the complex zeros of the following polynomial function. Write f in the factored form. F(x)=2x^4-5x^3-20x^2+115x-52
23. ### Algebra

Find the complex zeros of the following polynomial function. Write f in the factored form. F(x)=2x^4-5x^3-20x^2+115x-52
24. ### college algebra

find the complex zeros of the polynomial function. write f in factored form. f(x)=x^3-10x^2+37x-52
25. ### calculus

find the complex zeros of the polynomial function. write f in factored form. f(x)=x^3-10x^2+42x-72 please show work.

find the complete zeros of the polynomial function. Write f in factored form. f(x)=3x^4-10x^3-12x^2+122x-39 **Use the complex zeros to write f in factored form.** f(x)= Please show work
27. ### calculus

Find the complex zeros of the polynomial function. Write f in factored form. f(x)=3x^4-10x^3-12x^2+122x-39 Please show wrok, I do not understand how to do this.
28. ### Algebra

Use the rational zeros theorem to list the potential reational zeros of the polynomial function. Do not attempt to find the zeros. f(x)=6x^4+9x^3+30x^2+63x+28
29. ### Math-Polynomials/Zeros

How do I find complex zeros in a an equation if the equation doesn't have the + or - value at the end can th ecomplex zero(s) be made up? I'm getting really confused with complex zeros well zeros in general
30. ### algebra

Using the rational zeros theorem to find all zeros of a polynomial The function below has at least one rational zero. Use this fact to find all zeros of the function h(x)=7x^4-9x^3-41x^2+13x+6 if more than one zero, separate with commas. Write exact values, not decimal ...
31. ### algebra

Using the rational zeros theorem to find all zeros of a polynomial The function below has at least one rational zero. Use this fact to find all zeros of the function g(x)=5x©ù-28©ø-48x©÷-8x+7 if more than one zero, separate with commas. Write exact values, not decimal ...
32. ### Use the rational zeros theorem

Use the rational zeros theorem to list the potential reational zeros of the polynomial function. Do not attempt to find the zeros. f(x)=6x^4+9x^3+30x^2+63x+28
33. ### Polynomial Function

Could you help me with the following problem, I don't understand how to do it. Find an nth degree polynomial function with real coefficients satisfying the given conditions. 1. n=3; 3 and i are zeros; f(2)=20
34. ### college algebra

use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=x^3-8x^2-31x-22
35. ### pre calculus

use the rational zeros theorem to find all the real zeros of the polynomial function. use the zeros to factor f over the real numbers: f(x)=x^4+2x^3-7x^2-8x+12 I am totally lost, please help?
36. ### algebra

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)= x^4+6x^3-11x^2-24x+28 Molon
37. ### calculus

use rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=x^3-8x^2-31x-22 **please show work**
38. ### Pre-Calc

A polynomial function f(x) with real coefficients has the given degree, zeros, and solution point. Degree: 3 Zeros: -2,2+2√2i Solution Point: f(−1) = −68 (a) Write the function in completely factored form. (b) Write the function in polynomial form. Help Please my teacher...
39. ### College Algebra

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=2x^3-x^2+2x-1

Find all zeros of the following polynomial. Write the polynomial in factored form. f(x)=x^3-3x^2+16x-48 I put: x^2(x-3)+16(x=3) (x-3)(x^2+16) For zeros: x-3=0 x=0 **My teacher stated check the equation solution again. What is the value for x and hence what is the zero for the ...
41. ### Math

What does the degree of a polynomial expression tell you about its related polynomial function? Explain your thinking. Give an example of a polynomial expression of degree three. Provide information regarding the graph and zeros of the related polynomial function.
42. ### College algebra

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers f(x)=9x^4+28x^3+66x^2+196x+21 Find the real zeros of f Use the real zeros to factor f f(x)=
43. ### Math

A polynomial function with rational coefficients has the following zeros. Find all additional zeros. 2, -2 + ã10
44. ### college algebra

use rational zeros theorem to find all the real zeros in the polynomial function. use zeros to factor f over real numbers. f(x)=x^3+10x^2-13x-22 find real zeros of f? use real zeros to factor f?
45. ### Algebra

Suppose that a polynomial function of degree 5 with rational coefficients has​ 6, −2+4i, 4−sqrt2 as zeros. Find the other zeros. Thank you!
46. ### College algebra

Use the rationals theorem to find all the zeros of the polynomial function. Use the zeros to factor f over the real numbers, F(x)=7x^3-x^2+7x-1
47. ### Precalculus

Suppose that a polynomial function of degree 4 with rational coefficients has i and (-3 + square root of 3)as zeros find the other zeros
48. ### algebra

p(x)=x^3+2x^2-3x+20 one of this functions zeros is -4 When using synthetic division to find all the zeros of a polynomial function, would you plug in 4 or -4 into the actual equation?
49. ### pre-ap Algebra 2

write a polynomial function f of least degree that has the rational coefficients, a leading coefficient of 1, and the given zeros. Given zeros: -2,2,-1,3, sqrt 11
50. ### College algebra

Use the rationals theorem to find all the zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=x^3-2x^2-13x-10 x=
51. ### Pre Calculus

1. Find all rational zeros of the polynomial. Then determine any irrational zeros, and factor the polynomial completely. 3x^4-11x^3+5x^2+3x 2. Find the polynomial with leading coefficient 1 that has a degree of 4, a zero of multiplicity 2 at x=1 and a zero at x=2+i
52. ### Precalculus

Suppose that a polynomial function of degree 4 with rational coefficients has i and (-3 + square root of 3)as zeros find the other zeros show work please
53. ### college algebra

use the rational zeros theorem to find all the real zeros of the polynomial function,. use the zeros to factor f over the real numbers. f(x)=11x^3-x^2+11x-1 please show all work
54. ### PRECALC

find all the real and complex zeros of the polynomial P(x)=x^4 -2x^3 -2x^2-2x-3
55. ### Algebra

Consider the polynomial f(x) = 3x3 – 2x2 – 7x – 2. (a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (b) Find all of the zeros of the given polynomial. Be sure to show work, explaining how you have found them.
56. ### algebra

Consider the polynomial f(x) = 3x3 – 2x2 – 7x – 2. (a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (b) Find all of the zeros of the given polynomial. Be sure to show work, explaining how you have found them.
57. ### algebra

Consider the polynomial f(x) = 3x3 – 2x2 – 7x – 2. (a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (b) Find all of the zeros of the given polynomial. Be sure to show work, explaining how you have found them.
58. ### Rational Zeros

List all possible rational zeros for the polynomial below. Find all real zeros of the polynomial and factor f(x)=2x^4+19x^3+37x^2-55x-75
59. ### Algebra

Consider the polynomial: f(x) = 2x^3 – 3x^2 – 8x – 3. (a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (b) Find all of the zeros of the given polynomial. Be sure to show work, explaining how you have found them.
60. ### Math

Consider the polynomial f(x) = 2x^3 – 3x^2 – 8x – 3. (a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (b) Find all of the zeros of the given polynomial. Be sure to show work, explaining how you have found them.
61. ### Algebra

Could you please check my answers? Find an nth degree polynomial function with real coefficients satisfying the given conditions. 1. n=3; 3 and i are zeros; f(2)=20 -I got: f(x)=-4^3+12x^2-4x+12 3.n=3;4 and i zeros;f(-3)=60 -I got:f(x)=6x^3+24x^2+6x+24
62. ### math

If the digits of a number may be any one of 0 through 9 (except the first digit cannot be zero), and the system of alternating signs of coefficients is used to create a polynomial, what is the least number m of real zeros the polynomial can have? What is the greatest number M ...
63. ### math

If the digits of a number may be any one of 0 through 9 (except the first digit cannot be zero), and the system of alternating signs of coefficients is used to create a polynomial, what is the least number m of real zeros the polynomial can have? What is the greatest number M ...
64. ### math

If the digits of a number may be any one of 0 through 9 (except the first digit cannot be zero), and the system of alternating signs of coefficients is used to create a polynomial, what is the least number m of real zeros the polynomial can have? What is the greatest number M ...
65. ### rational zeros theorem

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=25x^4+26x^3+126x^2+130x+5 Find the real zeros x= Use the real zeros to factor f f(x)=
66. ### Math

Use the given information about a polynomial whose coefficients are real numbers to find the remaining zeros of the polynomial. Degree: 6 Zeros: -6 + 13i^3, -8 + s^2i, -3 - 4i
67. ### college algebra

1. solve the following logarithmic equation log_8(x+8)+log_8(x+7)=2 what is the exact solution 2.se the rational theorem to find all the real zeros of the polynomial function. use the zeros to factor f over the real numbers. f(x)=4x^4+5x^3+9x^2+10x+2 a.find the real zeros of f...
68. ### Finding polynomial from zeros

How to find the polynomial degree 2 and zeros are (1+i) & (1-i) I would like to see the steps to solve this. Thanks. If those are the roots, then the following are factors: (x-1-i)(x-1+i)
69. ### Math Problem2

List all possible rational zeros for the polynomial below. Find all real zeros of the polynomial below and factor completely. Please show all of your work. f(x) = 5x^4 – x^3 - 33x^2 – 43x – 16
70. ### Algebra

find the complex zeros of the polynomial. Write f in factored form: F(x)= 2x^2-5x^3-20x^2+115x-52=0
71. ### algebra

use the rational zero theorem to list the potential rational zeros of the polynomial function. Do not attempt to find the zeros. f(x)=2x^7-x^5+8x^4+52
72. ### pre cal

Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all the real zeros of the function. x^3 - 28x - 48 = 0 Value of x = -4 Please help!!Thank you

Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all the real zeros of the function. x^3 - 28x - 48 = 0 Value of x = -4 Please help!!Thank you
74. ### Math

f(x)=x64-4x^2+k. Find the values of k so thath the zeros of f satisfy the specified charachteristics. a.four real zeros b.two real zeros, each of multiplicity of two c.two real zeros and two complex zeros d.four complez zeros a.I don't know if this range goes for this or b. 1&...
75. ### Math (Complex Numbers)

how does one go about solving something such as: conjugate(z+2-3i) = z+5+10i Conjugates of actual complex numbers are very simple, but the inclusion of z trips me up
76. ### Math - Possible or Potential rational zeros

List all possible (or potential) rational zeros for the polynomial below. Find all real zeros of the polynomial below and factor completely over the real numbers. Please show all of your work. f(x) = x^4 - 7x^3 - 3x^2 + 19x + 14
77. ### Math

Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all the real zeros of the function. x^3 - 28x - 48 = 0 x=2 I have no idea how to start this problem!!
78. ### potential rational zeros

list the potential rational zeros of the polynomial function, do not find the zeros. f(x)=x^5-5x^2+4x+3
79. ### College Algebra

1.Give a quadratic function q(x) with a vertex of (-1, 2). 2. Give a function h(x) which does not have an inverse function. 3. Give a polynomial function g(x) with zeros 1,2,3 4. Give an exponential function s(x) passing through (0,2) and (4,1). 5. Give a rational function R(x...

I have two questions that I don't understand and need help with. 1. information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zerosof f. degree 4, zeros i;9+i 2. form a polynomial f(x) with real coefficients having the given degree ...
81. ### algebra

List all possible or potential rational zeros for the polynomial below find all real zeros of the polynomial below and factor completely over the real numbers. f(x) x^4 + 10x^3 + 12x^2 - 58x + 35 Someone anyone?????
82. ### pre cal

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 3, -13, and 5 + 4i Urgently need help
83. ### Precalc

The complex number -3 + 2i is one zero for a polynomial function. Which complex number must also be a zero for this function? -3 + 2i 3 + 2i -3 - 2i 3 - 2i I am very confused with what the question is exactly asking. Please help? Thanks
84. ### algebra

Form a polynomial f(x) with real coefficents having the given degree and zeros Degree 5; Zeros: 2; -i;-7+i Enter the polynomial f(x)=a(____) type expression using x as the variable
85. ### algebra 2

Write a polynomial function that has the zeros 2, -2, and -1 and has a leading coefficient of 1. Then graph the function to show that 2, -2, and -1 are solutions.
86. ### math

Find a polynomial f(x) with leading coefficient 1 and having the given degree and zeros. Each polynomial should be expanded from factored form, simplified and written in descending order of exponents on the variable. For example: (x+5)(x-2) should be given as the answer x^2 + ...
87. ### college algebra

form a polynomial f(x) with real coefficients having the given degree and zeros degree 4 zeros 5+3i;3 multiplicity 2 enter the polynomial f(x)=a?()

Find all the zeros of the function. When there is an extended list of possible rational zeros, use a graphing utility to graph the function in order to discard any rational zeros that are obviously not zeros of the function. (Enter your answers as a comma-separated list.) f(x...
89. ### Math

Multiply complex conjugates
90. ### math

use the rational zero theorem to find all the real zeros of the polynomial function. use the zeros to factor f over the real numbers: f(x)=4x^4+9x^3+30x^2+63x+14 I cant even find sample problems to help me figure this out. help me please?
91. ### algebra

form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros:-3 +5i; 2 multiplicity 2 enter the polynomial f(x)=a(?)
92. ### pre-calculus

form a polynomial f(x) with real coefficients having the given degree and zeros. degree 5; zeros -7; -i;-9+i enter the polynomial. f(x)=a(?)
93. ### math

What is an example of a quintic polynomial function that has exactly four zeros?
94. ### algebra

find zeros of a polynomial function
95. ### math

What is an example of a quintic polynomial function that has exactly four zeros?
96. ### math

what is an equation of a polynomial function that has zeros at -3 and -2?
97. ### math

what is an equation of a polynomial function that has zeros at -3 and -2?
98. ### algebra 2

What is the third–degree polynomial function such that f(0) = –18 and whose zeros are 1, 2, and 3
99. ### Math

I just wanted to double check that I am correct. 1.Find the zeros for the function: f(x)= 4(x-3)(x+2)(x-4)^2 Zeros are: 3,-2, 4(multiplicity 2) 2.Find the zeros for the function: f(x)= x^3-9x Zeros are: 0, 3, -3
100. ### Use the rationals theorem

Use the rationals theorem to find all the zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=2x^3-x^2+2x-1