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]
2 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]2 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
If john has 2 apples and gives sam 1 apple how many will john have ?
Effectus [21]

Answer:

1

Step-by-step explanation:

2-1=1

4 0
3 years ago
Write the first 4 terms of the sequence defined by the given rule f(n)=n2 -1
Softa [21]

Answer:

<h2>0, 3, 8, 15</h2>

Step-by-step explanation:

Substitute n = 1, n = 2, n = 3 and n = 4 to the equation f(n) = n² - 1:

f(1) = 1² - 1 = 1 - 1 = 0

f(2) = 2² - 1 = 4 - 1 = 3

f(3) = 3² - 1 = 9 - 1 = 8

f(4) = 4² - 1 = 16 - 1 = 15

5 0
3 years ago
Find the value of X. 40,x
Vilka [71]

Answer:

x = 70°

Step-by-step explanation:

x = one of the congruent angles in the triangle

Given angle measure: 40°

x = ? + ? = 180 - 40 = 140

x = 70

4 0
3 years ago
Read 2 more answers
Solve with elimination
Fittoniya [83]
I'm pretty sure this is correct

4 0
3 years ago
The swimsuit is on sale for 25% off its original price. If the original price was $58. What is the sale price?
sergiy2304 [10]

58.00 \div 10 \times 2 \div 2 \div 2
7 0
3 years ago
Other questions:
  • Jeff ran 2 miles in 12 minutes. Ju Chan ran 3 miles in 18 minutes. Did Jeff and Ju Chan run the same number of miles per minute?
    15·2 answers
  • What is the slope of the line that goes through the points (-2,0) and (-2,5)
    11·2 answers
  • A number expressible in the form a/b where a and b are integers
    14·1 answer
  • What is 16500 rounded to the nearest ten thousand
    14·1 answer
  • Please Help Me I Rally Need The Awnser
    13·1 answer
  • Which equation is tru when the value of x is 3.5?
    12·1 answer
  • 5)Write an algebraic equation for each statement, and then SOLVE for x
    9·1 answer
  • HELPP MEE PLEASEE! ILL TRY TO MARK U BRAINLIEST IF PEOPLE AINT SELFISH AND USE UP THE ANSWER BOXES
    7·1 answer
  • A string of length 160cm is cut into 2 pieces, in the ratio 3:5. Find the length of each piece​
    12·2 answers
  • Find the product of (4x − 3)(2x2 − 7x 1). 8x3 − 22x2 17x− 3 8x3 8x2 4x − 3 8x3 − 34x2 25x − 3 8x3 − 42x2 25x − 3.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!