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
Shkiper50 [21]
3 years ago
6

Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions.

Mathematics
1 answer:
lesya692 [45]3 years ago
5 0

Answer:

\displaystyle f(x) = -2(x-2)(x^2+4)

Step-by-step explanation:

We want to find a third degree polynomial with zeros <em>x </em>= 2 and <em>x</em> = 2i and f(-1) = 30.

First, note that by the Complex Root Theorem, since <em>x</em> = 2i is a root, <em>x</em> = -2i must also be a root.

Hence, we will have the three factors:

\displaystyle f(x) = a(x-(2))(x-(2i))(x-(-2i))

Where <em>a</em> is the leading coefficient.

Expand and simplify the second and third factors:

\displaystyle \begin{aligned} (x-(2i))(x-(-2i)) &= (x-2i)(x+2i) \\ \\ &= x(x-2i)+2i(x-2i) \\ \\ &= (x^2 - 2ix) + (2ix - 4i^2) \\ \\ &=x^2 + 4\end{aligned}

Hence:

\displaystyle f(x) = a(x-2)(x^2+4)

Since f(-1) = 30:

\displaystyle \begin{aligned}  f(x) &= a(x-2)(x^2+4) \\ \\ (30) &= a((-1)-2)((-1)^2+4) \\ \\ 30 &= -15a \\ \\ a&= -2\end{aligned}

In conclusion, third degree polynomial function is:

\displaystyle f(x) = -2(x-2)(x^2+4)

You might be interested in
Y-intercept = (0, 2)<br> slope = -3/7 what is the equation?
Marianna [84]

Answer:

y = -(3/7)x + 2

Step-by-step explanation:

(see attached)

recall that the slope-intercept form of a linear equation is

y = mx + b

where m = slope = given as -(3/7)

and b = y-intercept = 2

substituting these values into the eqation:

y = mx + b

y = -(3/7)x + 2

8 0
3 years ago
With reference to the figure, sin X equals?<br> 1.) 0.250<br> 2.)0.447<br> 3.)0.894<br> 4.)1
Flura [38]

Answer:

3.) 0.894

Step-by-step explanation:

✔️First, find BD using Pythagorean Theorem:

BD² = BC² - DC²

BC = 17.89

DC = 16

Plug in the values

BD² = 17.89² - 16²

BD² = 64.0521

BD = √64.0521

BD = 8.0 (nearest tenth)

✔️Next, find AD using the right triangle altitude theorem:

BD = √(AD*DC)

Plug in the values into the equation

8 = √(AD*16)

Square both sides

8² = AD*16

64 = AD*16

Divide both sides by 16

4 = AD

AD = 4

✔️Find AB using Pythagorean Theorem:

AB = √(BD² + AD²)

AB = √(8² + 4²)

AB = √(64 + 16)

AB = √(80)

AB = 8.9 (nearest tenth)

✔️Find sin x using trigonometric ratio formula:

Reference angle = x

Opposite side = BD = 8

Hypotenuse = AB = 8.944

Thus:

sin(x) = \frac{opp}{hyp} = \frac{8}{8.944} = 0.894 (nearest thousandth)

6 0
3 years ago
Sebastian and Mia want to buy a home valued at $250,000. The property tax for this location is 1%. Based on the current value of
denis-greek [22]
1% of $250,000 is $2,500

Your answer is C
5 0
3 years ago
Read 2 more answers
(02.02 HC) Arlene is comparing the prices of two truck rental companies. Company A charges $7 per hour and an additional $30 as
Elden [556K]
Solution in picture.

6 0
2 years ago
Luke has 75 Vbucks in his account he spends 5 Vbucks every 2 hours. At this rate how many hours did it take for all 75 V bucks t
mel-nik [20]

Answer:

30

Step-by-step explanation:

i did the math lol

7 0
2 years ago
Other questions:
  • Pls i need it like now
    12·1 answer
  • If 8 apples cost $1.60, how much is one apple?
    12·1 answer
  • I need to show work please i need help
    12·1 answer
  • // ANSWER PLS //
    15·1 answer
  • Help is appreciated ❤<br><br> Simplify the radical expression -2 √250
    15·1 answer
  • Answer please i will brainly
    10·1 answer
  • HELP ASAP. WILL GIVE BRAINLIEST! BEING TIMED!!!
    11·1 answer
  • Which of the following changes is a chemical change?<br> A ice me
    11·1 answer
  • A:Write (⅔)² in expanded form,<br> B. And then evaluate.
    11·1 answer
  • Hurt just hurry and answer please
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!