1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Paul [167]
3 years ago
10

1. Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial i

n standard form.
4, -8, and 2 + 5i


f(x) = x4 - 6x3 - 20x2 + 122x - 928

f(x) = x4 - 19x2 + 244x - 928

f(x) = x4 - 6x3 + 20x2 - 122x + 928

f(x) = x4 - 61x2 + 244x - 928
Mathematics
2 answers:
Katena32 [7]3 years ago
8 0
Polynomial with real coefficients always has even number of complex roots. We know that one of them is 2 + 5i so the second one will be  2 - 5i and:

f(x)=\big(x-4\big)\big(x-(-8)\big)\big(x-(2+5i)\big)\big(x-(2-5i)\big)=\\\\=(x-4)(x+8)(x-2-5i)(x-2+5i)=\\\\=(x^2-4x+8x-32)(x^2-2x+5ix-2x+4-10i-5ix+10i-25i^2)\\\\=\big(x^2+4x-32\big)\big(x^2-4x+4-25\cdot(-1)\big)=\\\\=(x^2+4x-32)(x^2-4x+29)=\\\\=x^4-4x^3+29x^2+4x^3-16x^2+116x-32x^2+128x-928=\\\\=\boxed{x^4-19x^2+244x-928}

Answer B.
Semmy [17]3 years ago
5 0

Answer:

Option 2 - f(x)=x^4-19x^2+244x-928          

Step-by-step explanation:

Given : Zeros of the polynomial 4, -8, and 2 + 5i.

To find : Write a polynomial function of minimum degree with real coefficients whose zeros include those listed ?

Solution :

The zeros of the polynomial are 4, -8, and 2 + 5i.

There is one conjugate exist i.e. 2-5i.

So, The polynomial form of zeros are      

f(x)=(x-4)(x+8)(x-(2+5i))(x-(2-5i))

f(x)=(x-4)(x+8)(x-2-5i))(x-2+5i))

Multiply the factors i.e. first two terms and other two terms multiply each other,

f(x)=(x^2+8x-4x-32)(x^2+5ix-2x-5ix-25i^2+10i-2x-10i+4)

f(x)=(x^2+4x-32)(x^2-4x+25+4)

f(x)=(x^2+4x-32)(x^2-4x+29)        

f(x)=x^4-4x^3+29x^2+4x^3-4x^2+116x-32x^2+128x-928      

f(x)=x^4-19x^2+244x-928          

Therefore, Option 2 is correct.                            

You might be interested in
if there is 2/3 of a bag of jelly beans, and Danny ate 1/4 of the bag last night, what fraction of the bag is left?
scoundrel [369]
2/3-1/4=5/12
You could make the denominators common by finding the GCF

The GCF of 4 and 3 is 12

This means that 8/12-3/12 which would give you 5/12.

:)
8 0
3 years ago
Read 2 more answers
Construct a grouped frequency distribution table for the ages of 30 teachers in a secondary school as recorded below : 26, 29, 2
Alina [70]

Answer:

I think you just put them In order

Step-by-step explanation:

And find the medium

3 0
3 years ago
Selina claims single having one exemption. Her state tax deduction is 21% of her federal tax contribution. Calculate the amount
Maurinko [17]

Based on the number of exemptions claimed by Selina and her biweekly gross pay, her state tax will be $16.80.

<h3>How much will Selina pay for state taxes?</h3>

Selina is to pay 21% of her federal taxes.

Seeing as she claims a single exemption and falls in the $840 to $860 bracket, the table shows that her federal tax contribution would be $80.

State taxes are therefore:

= 80 x 21%
= $16.80

Find out more on withholding allowances at brainly.com/question/11308445.

#SPJ1

4 0
1 year ago
Read 2 more answers
A cake mix calls for these ingredients. 2 cups of sugar 7 cups of flour 3 cups of milk 1 cup of oil Write the ratios of sugar to
Setler [38]

Answer:

Ratio of sugar and flour

2:7

Ratio of milk and oil

3:1

Step-by-step explanation:

Here in this question, we shall be writing ratios based on the given number of cups in the question.

We start with ratio of sugar to flour.

We have;2 cups of sugar and 7 cups of flour. Thus we have the ratio of sugar to flour as 2:7

Also we want the ratio of milk and oil

we have 3 cups of milk and 1 cup of oil

So the ratio of milk and oil is 3:1

5 0
3 years ago
Read 2 more answers
Algebra 1 - which equation represents exponential growth?
Nataly_w [17]

Answer:

d. y =5(1.06)^x

Step-by-step explanation:

growth formula is

y = (1+r)^t

1+r has to be greater than 1

mustangps

7 0
1 year ago
Other questions:
  • A library is to be built such that it is equidistant from the three towns . Describe how you can locate the construction site fo
    6·1 answer
  • Do you round 943 up or down
    10·2 answers
  • Please Hurry!!!
    5·1 answer
  • How do you solve (2z-3)(4z-7)=0
    14·2 answers
  • Please solve for y y(a-b)=c(y+a)
    12·1 answer
  • solve this system of linear equations. separate the x- and y-values with a comma. x = -42 - 8y -18x = -4 - 8y
    8·1 answer
  • Janice has car insurance that she must pay four times a year. If each payment is $156, how much money should she set aside each
    9·2 answers
  • Can anyone help with this?
    7·2 answers
  • Carla has a scooter worth $3,890. Her computer is worth $600. She owes $700 on her scooter and $497 on her credit card. Her pers
    14·2 answers
  • Please help me :,)<br><br>x=-2<br>x=-1<br>x=0<br>x=1<br>x=2​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!