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
Colt1911 [192]
3 years ago
8

Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities inclu

de those listed
2(multiplicity 2), 3 + i (multiplicity 1)
Mathematics
1 answer:
Softa [21]3 years ago
4 0

<u>Answer-</u>

<em>The polynomial function is,</em>

y=x^4-10x^3+38x^2-64x+40

<u>Solution-</u>

The zeros of the polynomial are 2 and (3+i). Root 2 has multiplicity of 2 and (3+i) has multiplicity of 1

The general form of the equation will be,

\Rightarrow y=(x-(2))^2(x-(3+i))(x-(3-i))   ( ∵ (3-i) is the conjugate of (3+i) )

\Rightarrow y=(x-2)^2(x-3-i)(x-3+i)

\Rightarrow y=(x^2-4x+4)((x-3)-i)((x-3)+i)

\Rightarrow y=(x^2-4x+4)((x-3)^2-i^2)

\Rightarrow y=(x^2-4x+4)((x^2-6x+9)+1)

\Rightarrow y=(x^2-4x+4)(x^2-6x+10)

\Rightarrow y=x^2x^2-6x^2x+10x^2-4x^2x+4\cdot \:6xx-4\cdot \:10x+4x^2-4\cdot \:6x+4\cdot \:10

\Rightarrow y=x^4-10x^3+14x^2+24x^2-40x-24x+40

\Rightarrow y=x^4-10x^3+38x^2-64x+40

Therefore, this is the required polynomial function.


You might be interested in
Solve for x and y. Geometry
Otrada [13]

Answer:

x =106.5

y = 73.5

Step-by-step explanation:

Angle x is 1/2 arc SPQ

x = 1/2(98+115)

x = 1/2(213)

x =106.5

We know that x+y = 180  since this is an inscribed quadrilateral in a circle

x+y=180

106.5 +y =180

Subtract 106.5 from each side

106.5-106.5 +y =180-106.5

y = 73.5

4 0
3 years ago
43 base five to base seven
solong [7]
First convert to decimal:

43_5=4\cdot5^1+3\cdot5^0=20+3=23

Now convert this to base 7:

\dfrac{23}7=3+\dfrac27
\dfrac27=0+\dfrac27
\implies23=43_5=32_7
7 0
3 years ago
Please give me the right answer. Expert help only.
son4ous [18]

Answer:

25 x 40 = 1000

1210 - 1000 = 210

210 / 45 = 4.66 hours

Step-by-step explanation:

7 0
2 years ago
A rectangular rug has a perimeter of 460 meters. The width of the rug is five meters more than 4 times the length. Find the
Paladinen [302]

Answer:

Length = 45 m

Width = 185 m

Step-by-step explanation:

Given:

Perimeter of rectangular rug = 460 m

width of the rug is five meters more than 4 times the length

To find:

Width and length of rug = ?

Solution:

Let the length = l m

As per given statement,

Width = 4l+5 m

Formula for perimeter of a rectangle = 2\times (Length +Width)

460=2\times (l+4l+5)\\\Rightarrow 230 = 5l+5\\\Rightarrow l = \dfrac{225}{5} = 45\ m

Width = 4l+5 m

Width = 4\times 45+5 = 185\ m

So, the answer is:

<em>Length = 45 m</em>

<em>Width = 185 m</em>

<em></em>

6 0
3 years ago
The coordinates of points A, B, and C are (5, 4), (–2, 1), and (4, –4), respectively. Which point, B or C, is closer to point A?
Elena-2011 [213]

Answer:

The distance between two points (x1,y1) and (x2,y2) = √((x1-x2)2+(y1-y2)2) Distance between A and B = √((5--2)2+(4-1)2) = √(72+32) = √(49+9) = √58 = 7.62 Distance between A and C = √(12+82) = √65 = 8.06 Point B is closer to A. Another method to solve this problem is to draw the points on a graph paper and measure distance with a ruler.

6 0
2 years ago
Read 2 more answers
Other questions:
  • Mona stopped at a gas station where the price per gallon was $2.80. She spent $14 to fill up her car. What equation would repres
    11·2 answers
  • At Emily’s closet 1/3 of the cloths are white and 1/5 are black what. What fraction of Emilly’s clothes are black and white ?
    13·2 answers
  • How many ten thousands in 2,689,456
    6·1 answer
  • What is the value of the express?
    13·1 answer
  • Can someone help me please
    5·2 answers
  • Give an example of a real number that is not rational.
    12·1 answer
  • Rs 600 will gave Rs 90 simple interest at 5 % per annum. ​
    7·1 answer
  • A group of students were given a spelling test
    5·2 answers
  • Suppose you have two empty accounts,A1 andA2. Each pays 8% APR. You put $100,000intoA1 now. One year from now you start making a
    15·1 answer
  • 0=9x-9x<br> no solution,<br> one solution,<br> infinite solutions
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!