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
butalik [34]
2 years ago
7

If 2i is a zero of f(x)=x^4+x^2+a, find the value of a

Mathematics
1 answer:
Sedbober [7]2 years ago
5 0

By the polynomial remainder theorem, because <em>x</em> = 2<em>i</em> is a zero of <em>f(x)</em>, we have no remainder upon dividing <em>f(x)</em> by <em>x</em> - 2<em>i</em>.

Computing the quotient yields

\dfrac{x^4+x^2+a}{x-2i} = x^3+2ix^2-3x-6i+\dfrac{12+a}{x-2i}

Then if the remainder term is 0, follows that <em>a</em> = -12.

You might be interested in
Current rules for telephone area codes allow the use of digits​ 2-9 for the first​ digit, and​ 0-9 for the second and third​ dig
Anna35 [415]

Using the fundamental counting theorem, we have that:

  • 648 different area codes are possible with this rule.
  • There are 6,480,000,000 possible 10-digit phone numbers.
  • The amount of possible phone numbers is greater than 400,000,000, thus, there are enough possible phone numbers.

The fundamental counting principle states that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are ways to do both things.

For the area code:

  • 8 options for the first digit.
  • 9 options for the second and third.

Thus:

8 \times 9 \times 9 = 648

648 different area codes are possible with this rule.

For the number of 10-digit phone numbers:

  • 7 digits, each with 10 options.
  • 648 different area codes.

Then

648 \times 10^7 = 6,480,000,000&#10;

There are 6,480,000,000 possible 10-digit phone numbers.

The amount of possible phone numbers is greater than 400,000,000, thus, there are enough possible phone numbers.

A similar problem is given at brainly.com/question/24067651

5 0
2 years ago
The height of a cone is twice the radius of its base. A cone has a height of 2 x and a radius of x. What expression represents t
notsponge [240]

Answer:

Let's Find it!

Step-by-step explanation:

So let's use the formula for the volume of a cone:

V=\pi r^{2} \frac{h}{4} \\V=\pi *x^{2} *\frac{1}{2} x\\V=\frac{1}{2} \pi x^{3}

So there you go!(you could also plug the things in google but thats okay)

Hope this Helps!

P.S. Stay Safe!

5 0
3 years ago
Read 2 more answers
Write an equation that is parallel to the line 4x - y = 2 and passes through the point (-2, 3)
sergeinik [125]
We can start from the given line's coefficients and translate the line from the origin to the given point.
  4(x -(-2)) -(y -3) = 0
  4x +8 -y +3 = 0

The equation of the desired line is ...
  4x -y = -11

_____
For standard form line ax+by=c, any parallel line will have only a different value of c. For c=0, the line goes through the origin (0, 0). To make it go through point (h, k) we can write it as
  a(x-h) +b(y-k) = 0
which is completely equivalent to
  ax +by = ah +bk

7 0
3 years ago
I need help ASAP please
lina2011 [118]
The answer will be x= 12.4
5 0
2 years ago
Read 2 more answers
Math questionnnnn thanks if you helop
kipiarov [429]

Answer:

13

Step-by-step explanation:

Replace X with 2

Evaluate the function. g(x) = 3x^2 – 2x + 5 Find f(2)​

g(x) = 3(2)^2 – 2(2) + 5

Next conduct PEMDAS

Exponents are first so solve 2^2 which is 2 x 2 = 4

g(x) = 3(4) – 2(2) + 5

Next step is multiplication multiply 3 x 4 and 2x2

g(x) = 12 – 4 + 5

conduct adding and subtracting left from right

g(x) = 13

3 0
3 years ago
Other questions:
  • Desmond wants to pay Andrea $5 more an hour than he pays Max. Desmond has a budget of $250. He has decided Andrea will work 10 h
    13·2 answers
  • The value of √222 is between which two integers?
    8·1 answer
  • How do you find 5% of 100 on a calculator?
    9·1 answer
  • Type the correct answer in the box.
    12·1 answer
  • Evaluate the expression when a=5 and b= -6 <br><br> -9b+a
    9·1 answer
  • Which is the graph of the function f(x) = x3 + x2 + 4?
    7·1 answer
  • Help needs to be done in 10 mins​
    5·1 answer
  • Suppose that c (x )equals 7 x cubed minus 70 x squared plus 13 comma 000 x is the cost of manufacturing x items. Find a producti
    8·2 answers
  • I need help with #3 plz
    12·2 answers
  • Suppose a balloon is filled with 5000 cm³ of helium. It then loses one fourth of its helium each day. How much helium will be le
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!