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
Yuliya22 [10]
3 years ago
13

Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and roots of 2-√6 , 2+ √6

, and 7-i
Mathematics
1 answer:
horsena [70]3 years ago
7 0

Answer:

x^{4} -18x^{3}+104x^{2} -172x-100

Step-by-step explanation:

The 3 roots are given out of which 2 are real and 1 is imaginary. For a polynomial of least degree having real coefficients, it must have a complex conjugate root as the 4th root. Therefore, based on 4 roots, the least degree of polynomial will be 4. Finding the polynomial having leading coefficient=1 and solving it based on multiplication of 2 quadratic polynomials, we get:  

\\\\x_{1} = 2-\sqrt{6} \\x_{2} = 2+\sqrt{6} \\x_{3}=7-i \\x_{4}=7+i \\\\P(x)=1(x-x_{1})(x-x_{2} )(x-x_{3} )(x-x_{4} ) \\\\=(x-(2-\sqrt{6}))(  x-(2+\sqrt{6} )) (x-(7-i))( x-(7+i))\\=((x-2)+\sqrt{6})( ( x-2)-\sqrt{6} ) ((x-7)+i)( (x-7)-i)\\=((x-2)^{2} -(\sqrt{6} )^{2} )((x-7)^{2}-(i)^{2})\\=(x^{2} -4x-2)(x^{2} -14x+50)\\=x^{4} -18x^{3}+104x^{2} -172x-100\\

You might be interested in
3. What is the perimeter of a 6-inch square?
nirvana33 [79]

Answer:

24

Step-by-step explanation:

6+6 =12

12+6 = 18

18+6 = 24

7 0
3 years ago
Read 2 more answers
These are questions 2-5 out of 20. are these correct!?
dusya [7]
I believe so, but It is kind of blurry for some reason on my screen but from what I can make out yes.
3 0
3 years ago
How man 1/3 cups make 3/4 cups
Sati [7]

Answer:

it would take 2.25 1/3 cups if you are looking for an exact answer, or if you are looking for the minimum amount of 1/3 cups necessary to make 3/4 it would be 3.

Step-by-step explanation:

You can solve this by cross multiplying 1/3 and 3/4

You will get 9/4 which simplifies to 2 1/4 or 2.25

8 0
2 years ago
There are 2.54cm in an inch, 12 inches in a foot, and 5,280 feet in a mile.which expression gives the number of centimeters in a
geniusboy [140]

Answer:

(2.54×12) ×5280

Step-by-step explanation:

Since there are 2.54cm in an inch, multiply 2.54 by 12 to find out how many cm there are in a foot. Then you multiply that by 5280

8 0
3 years ago
What is the perimeter of the figure?"
maksim [4K]

Answer:

14

Step-by-step explanation:

Perimeter= 4× 3.5 in

=14 in

5 0
3 years ago
Read 2 more answers
Other questions:
  • Ya yeet answer dis plzz
    10·2 answers
  • How to find tour next term in a sequence in fractions
    14·1 answer
  • What does 22 divided by 3 plus 1 equal?
    14·1 answer
  • 1. Is the product of √16 and 4/7 rational or irrational? Explain your reasoning.
    6·2 answers
  • Kathy's kitchen serves 3 pieces of bacon with every 2 eggs.If the restaurant served 42 eggs at breakfast, how much bacon did the
    9·1 answer
  • What is the area of a circle with a radius of 87.1 cm?​
    7·2 answers
  • Find the value of x.<br> A. 70<br> B. 30<br> C. 65<br> D. 40
    14·1 answer
  • 2. If r=7 is a solution to -6r+18=k(x-15), then which of the following must be the value of K?
    13·1 answer
  • The next question(s) are based on this scenario: A researcher randomly assigned boys and girls to each of two groups. One group
    8·1 answer
  • Yuto has a bag containing 3 red marbles, 5 blue marbles, 2 green marbles, and 8 yellow marbles. Rin reaches into the
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!