A factorization of 
is 
.
<h3>What are the properties of roots of a polynomial?</h3>
- The maximum number of roots of a polynomial of degree
is . - For a polynomial with real coefficients, the roots can be real or complex.
- The complex roots of a polynomial with real coefficients always exist in a pair of conjugate numbers i.e., if
is a root, then 
is also a root.
If the roots of the polynomial 
are 
, then it can be factorized as 
.
Here, we are to find a factorization of 
. Also, given that 
and 
are roots of the polynomial.
Since is a polynomial with real coefficients, so each complex root exists in a pair of conjugates.
Hence, 
and 
are also roots of the given polynomial.
Thus, all the four roots of the polynomial , are: 
.
So, the polynomial can be factorized as follows:
![\{x-(-2+i\sqrt{7})\}\{x-(-2-i\sqrt{7})\}\{x-(1-i\sqrt{3})\}\{x-(1+i\sqrt{3})\}\\=(x+2-i\sqrt{7})(x+2+i\sqrt{7})(x-1+i\sqrt{3})(x-1-i\sqrt{3})\\=\{(x+2)^2+7\}\{(x-1)^2+3\}\hspace{1cm} [\because (a+b)(a-b)=a^2-b^2]\\=(x^2+4x+4+7)(x^2-2x+1+3)\\=(x^2+4x+11)(x^2-2x+4)](https://tex.z-dn.net/?f=%5C%7Bx-%28-2%2Bi%5Csqrt%7B7%7D%29%5C%7D%5C%7Bx-%28-2-i%5Csqrt%7B7%7D%29%5C%7D%5C%7Bx-%281-i%5Csqrt%7B3%7D%29%5C%7D%5C%7Bx-%281%2Bi%5Csqrt%7B3%7D%29%5C%7D%5C%5C%3D%28x%2B2-i%5Csqrt%7B7%7D%29%28x%2B2%2Bi%5Csqrt%7B7%7D%29%28x-1%2Bi%5Csqrt%7B3%7D%29%28x-1-i%5Csqrt%7B3%7D%29%5C%5C%3D%5C%7B%28x%2B2%29%5E2%2B7%5C%7D%5C%7B%28x-1%29%5E2%2B3%5C%7D%5Chspace%7B1cm%7D%20%5B%5Cbecause%20%28a%2Bb%29%28a-b%29%3Da%5E2-b%5E2%5D%5C%5C%3D%28x%5E2%2B4x%2B4%2B7%29%28x%5E2-2x%2B1%2B3%29%5C%5C%3D%28x%5E2%2B4x%2B11%29%28x%5E2-2x%2B4%29)
Therefore, a factorization of is .
To know more about factorization, refer: brainly.com/question/25829061
#SPJ9
Answer: radius = 19.99 centimeters
Step-by-step explanation:
The formula for determining the volume of a cylinder is expressed as
Volume = πr²h
Where
r represents the radius of the cylinder.
h represents the height of the cylinder.
π is a constant whose value is 22/7
From the information given,
Volume = 16328 cubic centimeters
Height = 13 centimeters
Therefore,
16328 = 22/7 × r² × 13
16328 = 40.857r²
Dividing the left hand side and the right hand side of the equation by 40.857, it becomes
r² = 16328/40.857 = 399.6378
Taking square root of the left hand side and the right hand side of the equation, it becomes
r = 19.99 centimeters
the answer is 13/7 and here is the correct question
the answer is 13/7 and here is the correct questionwhen a customer wants pie for dessert you cut a whole pies into 7 equal slices...at the end of your shift 3/7 of. a cherry pie.2/7. of an apple pie.3/7 of a peach pie.and 5/7 of a blueberry pie remain...How much pie remains as a fraction of. a whole pie...
Answer:
13/7
Step-by-step explanation:
From the question, we have
3/7 of cherry pie
2/7 of apple pie
3/7 of peach pie
5/7 of blueberry pie
Now we have to add up all of these in order to get the total amount of pie
3/7 + 2/7 +3/7 +5/7
= (3+2+3+5)/7
=13/7
If expressed as a mixed fraction
= 1 6/7
In conclusion, 13/7 pie remains as a fraction of a whole.
Answer:
The 95% confidence interval for the percent of all black adults who would welcome a white person into their families is (0.8222, 0.8978).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of 
.
For this problem, we have that:
323 blacks, 86% of blacks said that they would welcome a white person into their families. This means that 
95% confidence level
So 
, z is the value of Z that has a pvalue of 
, so 
.
The lower limit of this interval is:
The upper limit of this interval is:
The 95% confidence interval for the percent of all black adults who would welcome a white person into their families is (0.8222, 0.8978).
