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
Triss [41]
3 years ago
7

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the zeros 4 and 3−

i.
Mathematics
1 answer:
Neko [114]3 years ago
5 0

Answer:

P(x) = x^3 - 10x^2+ 34x-40

Step-by-step explanation:

Given

p =1 -- Leading coefficient

Zeros: 4\ and\ 3  - i

Required

Determine the polynomial

Represent the zeros with a and b

Such that

a = 4

b = 3 - i

The polynomial is:

P(x) = p * (x - a) * (x - b)

P(x) = 1 * (x - 4) * (x - (3 - i))

However, to solve further: We need to symmetrise over 3-i  and its conjugate

P(x) = 1 * (x - 4) * (x - (3 - i))* (x - (3 + i))

P(x) =  (x - 4) * (x - (3 - i))* (x - (3 + i))\\\\

To define a suitable function, the expression becomes

P(x) =  (x - 4) * ((x - 3)^2+1)

P(x) =  (x - 4) * ((x - 3)(x - 3)+1)

P(x) =  (x - 4) * (x^2 - 6x + 9+1)

P(x) =  (x - 4) * (x^2 - 6x +10)

Open bracket

P(x) = x^3 - 6x^2 +10x - 4x^2 + 24x-40

P(x) = x^3 - 6x^2  - 4x^2+10x + 24x-40

P(x) = x^3 - 10x^2+ 34x-40

You might be interested in
company A sold 6,028,468 cans of corn during the last three months. What is the value of the digit 4 in the number 6,028,468?
balu736 [363]
The value of the digit 4 in the number 6,028,468 is 100
4 0
3 years ago
CHORES Wayne raked 30 bags of leaves in 3 hours. If he raked the same number of bags each hour, how many bags of leaves did he r
zubka84 [21]

divide total bags by number of hours

30 bags / 3 hors = 10 bags per hour

 he racked 10 bags per hour

7 0
3 years ago
Read 2 more answers
Ratio for the volumes of two similar pyramids, given that the ratio of their edge lengths is 8:3?
emmasim [6.3K]
All you have to do is divide the left side of the ratio by 5 and the right side of the ratio by 7. The one that comes out even on both sides is the correct one.
6 0
3 years ago
PLEASE HELP! WILL GIVE BRAINLIEST!!!!!
Sophie [7]

The 8 percent commission must be at least $1000.

8% = $1000

1% = $125

100% = $12500

Hence, Jim needs to sell $12500 dollars worth of widgets.

6 0
3 years ago
Nicolas weighs 37 kilograms 95 grams. Jacques weighs 4,650 grams less than Nicolas. How much does Jacques weigh?
slava [35]

Step-by-step explanation:

convert to g

37 095 g

37 095-4650=32 445 g / 32.455 kg

3 0
3 years ago
Other questions:
  • Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and th
    9·1 answer
  •  Can someone plz help me What is the surface area of the figure?     A. 408 ft2   B. 458 ft2   C. 545 ft2   D. 720 ft2
    8·2 answers
  • How can a ratio's number can be changed without changing the ratio itself
    10·1 answer
  • A store manager ordered 28 crates of mangoes.There were 36 mangoes in each crate.WHEN the mangoes were delivered, he sold the ri
    14·1 answer
  • What is 02.15cm in meters
    7·1 answer
  • Ashley puts 45 stamps in an album. She puts the same number of stamps on each page,and 3 stamps on the last page. There are 2 mo
    12·1 answer
  • What is the measure of a
    13·2 answers
  • Can someone help me find an equation for both of these ❤️
    10·1 answer
  • Andy constructed a triangle. Angle 1 and 2 are the same size and angle 3 has a measurement of 100 degrees. What is the measureme
    9·1 answer
  • 1. What value of x makes the equation 3x - 6 = 9 true?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!