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
jeka57 [31]
3 years ago
8

Consider the polynomial p(x) = x^3 + 4x^2 + 6x − 36.

Mathematics
1 answer:
Nady [450]3 years ago
4 0

Answer:

a. attached graph; zero real: 2

b. p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)

c. the solutions are 2, -3-3i and -3+3i

Step-by-step explanation:

p(x) = x³ + 4x² + 6x - 36

a. Through the graph, we can see that 2 is a real zero of the polynomial p. We can also use the Rational Roots Test.

p(2) = 2³ + 4.2² + 6.2 - 36 = 8 + 16 + 12 - 36 = 0

b. Now, we can use Briott-Ruffini to find the other roots and write p as a product of linear factors.

2 |  1     4     6    -36

     1      6    18     0

x² + 6x + 18 = 0

Δ = 6² - 4.1.18 = 36 - 72 = -36 = 36i²

√Δ = 6i

x = -6±6i/2 = 2(-3±3i)/2

x' = -3-3i

x" = -3+3i

p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)

c. the solutions are 2, -3-3i and -3+3i

You might be interested in
Students surveyed about birthdays. How many more students were born on monday than friday?
Varvara68 [4.7K]
C) 2 students
Explanation
Take Monday’s amount and subtract Friday’s
3-1=2
3 0
3 years ago
Find the perimeter. Round to the nearest whole number.<br> 15 is c and 30 is a)
ziro4ka [17]

Answer:

45

Step-by-step explanation:

Hope this helps.

8 0
3 years ago
1000*0+321*15678*9(-4563)
Vikki [24]

Answer:

-206675344746

Step-by-step explanation:

1000*0+321*15678*9(-4563) = -206675344746

7 0
3 years ago
Read 2 more answers
Ms. Jan brought in cookies of her class. She gave out half of them in the morning. At lunch, she gave out 12 more. She then had
Svetach [21]

Answer:

Jan brought 44 cookies

Step-by-step explanation:

To solve this problem, we need to work backwards. First, we have 10 cookies left at the end of the day. At lunch, she gave away 12 cookies. This means that Ms. Jan had 22 cookies at lunch since  

10 + 12 = 22

In the morning, Ms. Jan gave out half of her cookies. This means that she started with twice as many cookies as she had at the beginning of lunch.  

22  x 2 = 44

Ms. Jan brought 44 cookies.

7 0
3 years ago
PLEASE HELP ME FAST!!!! ( It's about y-intercept)
Hoochie [10]

Answer:

y = 6x -7

Step-by-step explanation:

1. The equation of any line in slope-intercept form is y = mx + b, where y = y-coordinate, m = slope, x = x-coordinate, and b = y-intercept.

2. Given that the slope is 6, we plug that value in m, and given that the y-intercept is -7, we plug that value in b:

  • y = mx + b
  • y = 6x - 7
5 0
3 years ago
Other questions:
  • Does anyone know this?
    10·2 answers
  • Let b = 2 Evaluate 4 ⋅ (8 − b)b
    11·2 answers
  • Jackson wants to divide a
    10·1 answer
  • WILL GIVE BRAINLY PLEASE HELP!!!!!!!
    15·1 answer
  • A line the contains the point (-3,6) and (5,10)
    9·1 answer
  • A clock chimes once at 1, twice at 2
    14·1 answer
  • This year, 12,376 phone calls were made for an annual fund raising event.last year ,9,009 phone calls were made.How many more ca
    12·2 answers
  • What is the LCD of 4 and 5?<br><br> 13<br> 21<br> 42<br> 36
    11·2 answers
  • Use the distributive property to simplify the expression.
    14·1 answer
  • Rounding off to the nearest thousand<br><br> 1627=?????
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!