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
umka21 [38]
3 years ago
9

Find all three distinct roots for X³ =1. (two of them are complex mumber). And show that sum of all roots is zero.​

Mathematics
1 answer:
liraira [26]3 years ago
8 0

<em>x</em> ³ = 1

<em>x</em> ³ - 1 = 0

<em>x</em> ³ - 1³ = 0

Factorize the right side as a difference of cubes:

(<em>x</em> - 1) (<em>x</em> ² + <em>x</em> + 1) = 0

Then

<em>x</em> - 1 = 0   <u>or</u>   <em>x</em> ² + <em>x</em> + 1 = 0

The first equation yields <em>x</em> = 1 as a root.

For the other equation, rearrange and complete the square to get the other two roots,

<em>x</em> ² + <em>x</em> + 1/4 = -3/4

(<em>x</em> + 1/2)² = -3/4

<em>x</em> + 1/2 = ±√(-3/4) = ± <em>i</em> √3/2

<em>x</em> = -1/2 ± <em>i</em> √3/2

<em>x</em> = (-1 ± <em>i</em> √3)/2

Since complex roots occurs in conjugate pairs, taking the sum of these two roots eliminates the imaginary part:

(-1 + <em>i</em> √3)/2 + (-1 - <em>i</em> √3)/2 = (-1 - 1)/2 = -2/2 = -1

and adding to 1 indeed shows that the sum of roots is zero.

You might be interested in
What's the answer to this questions?
tia_tia [17]
I believe the answer is 2 :) .
6 0
2 years ago
Can someone help me with this problem. I don’t know how to do volume.
densk [106]

Answer:

7.5in³

Step-by-step explanation:

1x5x1.5=7.5

7 0
3 years ago
A) NO CHANGE
ollegr [7]

The most appropriate choice for sentence correction will be given by:

<h3>What is sentence correction?</h3>

Sentence correction is a type of grammatical practice where a sentence is given with a word or a phrase that requires grammatical changes or improvement.

Now,

  • In the given sentence, "Wilmers and Estes caution, however, that <u>having more otters</u> will not automatically solve the problem of higher levels of carbon dioxide in the air".
  • The most appropriate choice for sentence correction will be given by: the otters multiplying (option B).

To learn more about sentence correction, refer to the link: brainly.com/question/14632568

#SPJ4

6 0
1 year ago
2(c-5) - 3<br> What is the answer?
Sveta_85 [38]

Step-by-step explanation:

2 · c - 5 · 2 - 3 = 2c - 10 - 3

2c - 10 - 3 = 2c - 7

7 0
3 years ago
Find excluded values
denpristay [2]

\frac{5x-20}{14x^{2}-7x }

6 0
3 years ago
Other questions:
  • 21. Write the equation of a line that is perpendicular to the given line and that passes through the given point.
    15·1 answer
  • 1/2 + 1/3= whats the answer
    12·2 answers
  • 9*7/2*6*1-3*876+12,557,000
    8·1 answer
  • How to find the unknown length of right triangle
    9·1 answer
  • = 3x + 4, what is y when x is 1, 2, and 3
    8·1 answer
  • What is the opposite of squaring a number (e.g. x2 )?​
    13·2 answers
  • 4.75 qt = fl oz. pls help me with complete answers
    9·1 answer
  • 4. A movie-streaming service offers 12 children's movies. This is 15% of the
    10·1 answer
  • Y = 2x + 3 find the 151st term
    13·1 answer
  • Simplify this expression<br> <img src="https://tex.z-dn.net/?f=%5Cfrac%7B%28a%5E8a%5E6%29%7D%7Ba%5E2%7D%20%5E%5Cfrac%7B1%7D%7B7%
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!