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
zheka24 [161]
3 years ago
5

Find all roots given that x = 3 + i is a solution. x^4 - 10x^3 + 29x^2 - 10x - 50 = 0

Mathematics
1 answer:
Basile [38]3 years ago
5 0

Answer:

x = 3 + i, x = 3 - i , x = 5 , and x = -1

Step-by-step explanation:

We know that given the polynomial with real coefficients, if x = 3 + i is a root, then x = 3 - i must be another root. These two roots can combine multiplicative factors as shown:

(x - 3 - i) * (x - 3 + i) = (x-3)^2 + 1 = x^2 - 6 x + 9 + 1 = x^2 - 6 x + 10

Then we divide the given polynomial: x^4 - 10x^3 + 29x^2 - 10x - 50  by the quadratic one we just found, and get a perfect division:

{x^4 - 10x^3 + 29x^2 - 10x - 50} / {x^2 - 6 x + 10} = x^2 - 4 x - 5

which can be factored out by grouping as shown below:

x^2 - 4 x - 5 = x^2 - 5 x + x - 5 = x (x - 5) + x - 5 = (x - 5 ) * (x + 1)

then the full factor form of the quartic polynomial given is:

(x - 3 - i) * (x - 3 + i) * (x - 5 ) * (x + 1)

and therefore the associated roots are:

x = 3 + i, x = 3 - i , x = 5 , and x = -1

You might be interested in
The museum charges $14 for adult admission and $11 for each child. the museum bill for a school field trip was $896.
lord [1]
14x + 11y = 896

x = number of adults
y= number of kids
if nine adults went then 70 kids went
6 0
3 years ago
What is the measure of AB in O below?
8_murik_8 [283]

Answer:

The measure of an arc is equal to the angle opposite it

Therefore the answer is C. 100°

Hope this helps!

8 0
3 years ago
I need help with this​
Fynjy0 [20]

Answer:

a stationary sells 8pencil for the cost price of 10pencil find his gain percent

5 0
3 years ago
What is the range of the function graphed below?<br> A. 1_ B. -3 C. -2_ D. -3_
kap26 [50]
It would be B because it does to -3
3 0
2 years ago
Read 2 more answers
Burj l Arab Hotel,one of the world's tallest buildings,was finished in 1999.Located in Dubai,it is 1,053 feet high with 60 stori
AlexFokin [52]

Each floor is 3.35 feet taller than each floor of the Aon Center


5 0
3 years ago
Other questions:
  • The sum of the measures of the angles of any triangle is 180 degrees . In a certain triangle, the largest angle measures 55 degr
    12·1 answer
  • 3 sin^{2} x +cos 2x= (5/4)<br>answer in radians
    15·1 answer
  • Car X travels 144 miles in 3 hours.
    5·1 answer
  • X^2-7x+10=0?? Please and thank you
    5·1 answer
  • Identify two solutions to the function: f(x) = 2(3)​
    8·1 answer
  • Please help meeeeeeee​
    6·1 answer
  • PLS HELP (LAST QUESTION)
    15·1 answer
  • The length of a diagonal of a square is 72cm. find the length of the sides of the square​
    13·1 answer
  • Someone pls help me answer this pls
    14·2 answers
  • When simplified, 9x-(x+4) is what
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!