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
Nikolay [14]
3 years ago
8

Write a polynomial of degree 5 with zero x=0,i square root 7, -2i

Mathematics
1 answer:
professor190 [17]3 years ago
7 0

Answer:

P(x)=x^5+11x^3+28x

Step-by-step explanation:

<u>Roots of a polynomial</u>

If we know the roots of a polynomial, say x1,x2,x3,...,xn, we can construct the polynomial using the formula

P(x)=a(x-x_1)(x-x_2)(x-x_3)...(x-x_n)

Where a is an arbitrary constant.

We know three of the roots of the degree-5 polynomial are:

x_1=0;\ x_2=\sqrt{7}\boldsymbol{i}:\ x_3=-2\boldsymbol{i}

We can complete the two remaining roots by knowing the complex roots in a polynomial with real coefficients, always come paired with their conjugates. This means that the fourth and fifth roots are:

x_4=-\sqrt{7}\boldsymbol{i}:\ x_3=+2\boldsymbol{i}

Let's build up the polynomial, assuming a=1:

P(x)=(x-0)(x-\sqrt{7}\boldsymbol{i})(x+\sqrt{7}\boldsymbol{i})(x-2\boldsymbol{i})(x+2\boldsymbol{i})

Since:

(a+b\boldsymbol{i})\cdot (a-b\boldsymbol{i})=a^2+b^2

P(x)=(x)(x^2+7)(x^2+4)

Operating the last two factors:

P(x)=(x)(x^4+11x^2+28)

Operating, we have the required polynomial:

\boxed{P(x)=x^5+11x^3+28x}

You might be interested in
100 POINTS!!!
jenyasd209 [6]

Answer:

It's actually an  enlargement  of the figure.

Step-by-step explanation:

Because if the figure originally was M' (-2,2), S' (4,2), V' (2, -2). And now the shape is M (-3, 3), S (6, 3), V ( 3, -3). This means that the Triangle got bigger.

The scale factor of the smaller shape inside of the bigger shape is 2 and the scale factor of the bigger shape is 3 making the bigger shape well bigger.

5 0
3 years ago
Which rational number could be graphed between -3 and -4
Snezhnost [94]

Answer:

-3.5

Step-by-step explanation:

An example is -3.5.

3 0
3 years ago
Read 2 more answers
Explanation how solve step by step 2/7m-1/7=3/14
Drupady [299]

Answer:

m = 25/28

Step-by-step explanation:

It's best to enclose fractional coefficients inside parentheses to eliminate ambiquity:   2/7m-1/7=3/14 => (2/7(m - (1/7) = (3/14).

The LCD is 14; each of the denominators {7, 14} divides evenly into 14.  Hence our equation becomes

(4)(m - 1/7) = 3

... after multiplying every term by 14.

Let's multiply each side by 7 to eliminate the remaining fraction:

4(7m - 1) = 21, or

28m - 4 = 21, or

28m = 25.

Hence, m = 25/28.

8 0
4 years ago
Which system has no solutions?
seraphim [82]

Answer:

2nd option

y > 6 and y < 2

Step-by-step explanation:

as the value of y can not be greater than 6 and less than 2 at the same time, the 2 inequalities have no common solutions

theefore no solution

8 0
3 years ago
Two buses leave a station at the same time and travel in opposite directions. One bus travels 15 /kmh faster than the other. If
Nat2105 [25]
Since the buses travel in opposite directions, the speed at which they distance themselves is the sum of their speeds.
One bus travels at speed s.
The other bus travels at speed s + 15.
The sum of the speeds is s + s + 15 = 2s + 15

speed = distance/time

distance = speed * time

366 = (2s + 15) * 2

183 = 2s + 15

168 = 2s

s = 84

The slower bus travels at 84 km/h.

s + 15 = 84 + 15 = 99

The faster bus travels at 99 km/h.

Check:
In 2 hours, the slower bus travels 2 * 84 km = 168 km
In 2 hours, the faster bus travels 2 * 99 km = 198 km
In 2 hours, the buses are 198 km + 168 km = 366 km apart.
Our answer is correct.
6 0
3 years ago
Other questions:
  • What is the end behavior of f(x)=5x^3-2x+5
    10·2 answers
  • 65% of what is 39? ​
    15·2 answers
  • Matias solved 28 math problems in 20 minutes yesterday. Using the same rate, how many math problems can Matias solve in 90 minut
    8·2 answers
  • 3(x – 2) + 4x = 10(x + 1)<br><br> ( 25 pts 4 answering right)
    12·2 answers
  • Sarah describes the following situation: When fertilizer was added to one plant and nothing was added to the other plant, there
    7·2 answers
  • Sum of two number is 120. If the larger number is four times the smaller number, wbat are the two numbers
    11·1 answer
  • A triangle has side length of 10 inches, 24 inches, and 26 inches. Is the triangle a right triangle?
    13·1 answer
  • start at -3.5 and then add to that 4.2. As if you were walking from -3.5 on the number line up 4.2 steps to the right. Where wou
    5·2 answers
  • Can someone please help me with questions 12 through 14 with the answer correct I was trying but I don’t know what I put down is
    10·1 answer
  • Help please : -5+6/3 + 3+6/-5 =
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!