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
Lana71 [14]
3 years ago
14

Let f be a functions of degree 4 whose coefficients are real numbers: two of its zeros are - 3 and 4 - i. Explain why one of the

remaining zeros must be a real number. Write down one of the missing zeros.
Mathematics
1 answer:
kvasek [131]3 years ago
8 0

Answer:

Step-by-step explanation:

We have the following theorem, if f is a polynomial with real coefficients, we can factor it completely in factors of the degree at most 2.

Consider first a polynomial of degree two, hence it is a polynomial of the form ax^2+bx+c. The cuadratic formula tells us that the solutions are of the form

x = \frac{-b\pm \sqrt[]{b^2-4ac}}{2a}.

Note that square root, over the reals, tells us that the are only real solutions if b^2-4ac \geq 0. If that is not the case, say it's negative, the solution are complex. Then, the solutions are of the form

x = \frac{-b \pm i \sqrt[]{4ac-b^2}}{2a}. NOte that this means that if we have a complex number of the form a+bi that is a solution, then the number a-bi (who is called the complex conjugate) is also a solution.

Recall that when we have a polynomial f(x) whose a zero is the number c, then we can factor f as follows f(x) = (x-c) * p(x) where p(x) is another polynomial of lesser degree .

So far, we know that -3 and 4-i are zeros of the function f. Note that we are missing two zeros. But, since complex numbers are zeros of polynomial only by pairs (that is the number and its conjugate are zeros), then, we must have that one of the missing 2 zeros is a real number. We have 4-i as a zero, then, its complex conjugate must be also a zero, i.e 4+i is a zero.

You might be interested in
How do you find the volume of a cardboard box this is 12 cm long, 2cm wide and 3 cm high?
levacccp [35]
V = 12 × 2 × 3 = 72 cm3
Hope this helps!
7 0
3 years ago
Please help me I don’t get this at all thank you
faust18 [17]

Answer:

80 ft

Step-by-step explanation:

Perimeter is adding the lengths of all the sides.

6 0
3 years ago
Read 2 more answers
cos2x=____. Check all that apply. A. 1-2sin^2 x. B. 2sin^2 x-1. C. sin^2 x-cos^2 x. D. cos^2 x-sin^2 x
g100num [7]
         cos 2 x = cos² x - sin² x = 1 - sin² x - sin² x = 1 - 2 sin² x.
         Answer: A ) 1 - sin² x and D ) cos² x - sin² x 
       
 Thank you.
7 0
2 years ago
Read 2 more answers
Ok so brainly wont let me post the questions so I'm putting them in the comments but 100 points and brainlyest to the person who
Degger [83]

Answer:

here are the answers

Step-by-step explanation:

Part A)

scientific notation ------>  

standard notation ----->  

Part B)

scientific notation ------>  

standard notation ----->  

Part C)

scientific notation ------>  

standard notation ----->  

Part D)

scientific notation ------>  

standard notation ----->  

Part E)

scientific notation ------>  

standard notation ----->  

4 0
3 years ago
triangle ABC is reflected about the line Y equals negative X to give triangle ABC with vertices A (-1, 1), B (-2, -1), C (-1,0).
Amiraneli [1.4K]

9514 1404 393

Answer:

  • A'(-1, 1)
  • B'(1, 2)
  • C'(0, 1)

Step-by-step explanation:

Reflection across the line y = -x is accomplished by the transformation ...

  (x, y) ⇒ (-y, -x)

Then the images of the given points are ...

  A(-1, 1) ⇒ A'(-1, 1) . . . . this point is on the line of reflection, so doesn't move

  B(-2, -1) ⇒ B'(1, 2)

  C(-1, 0) ⇒ C'(0, 1)

7 0
2 years ago
Other questions:
  • Margaret goes to the county fair with $35. Rides cost $3 each. Write an equation that gives the amount of money m that Margaret
    12·2 answers
  • Tamiko got a check for 109.60 and a small bonus check for 34.15.What is the net result of her transactions using the result from
    15·1 answer
  • PLEASE PLEASE PELASE SOMEONE HELO ME ON 4 AND 5 OKEASE HELP ME DIND X AND Y IM FREAKINF OUT THIS IS DUE AT 2
    5·1 answer
  • The triangles are similar. Find the value of x. Show all work
    12·2 answers
  • What is the first step in solving for w in the equation 3W + 5 = 14?
    5·1 answer
  • In degree measure, the angles pie/3, pie/4, and pie/2 are respectively
    11·1 answer
  • Need help with 7, 8, and 9 plz :]
    15·1 answer
  • Using the information given, write an equation in slope-intercept form.
    12·2 answers
  • Determine whether the given sequence could be geometric, arithmetic, or neither. If possible identify the common ratio or common
    7·1 answer
  • Helppp look at photo will mark brainliest
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!