The value of algebraic multiplicity will be 1 and geometric multiplicity will be 1
[tex]$$\begin{aligned}& A=\left[\begin{array}{ccc}3 & -2 & 0 \\-2 & 4 & 4 \\1 & 0 & 2\end{array}\right] \\& \Rightarrow A=\left[\begin{array}{ccc}-1 & 1 & 0 \\0 & 0 & 0 \\1 & 1 & -2\end{array}\right]\end{aligned}$$[/tex]
[tex]$$Det(A-\lambda I) = Det A=\left[\begin{array}{ccc}(-1-\lambda) & 1 & 0 \\0 & -\lambda & 0 \\1 & 1 & (-2-\lambda)\end{array}\right]$$[/tex]
[tex]$$-(1+\lambda)\left|\begin{array}{cc}-\lambda & 0 \\1 & -2-\lambda\end{array}\right|-1\left|\begin{array}{cc}0 & 0 \\1 & -2-\lambda\end{array}\right|$$[/tex]
[tex]$$\begin{aligned}& =-(1+\lambda)\left(\lambda^2+2 \lambda\right) . \\& =-\lambda(1+\lambda)(\lambda+2) .\end{aligned}$$[/tex]
So, for [tex]\lambda=-1[/tex], eigen values are [tex]\lambda[/tex]=0,-1,-2.
Hence, the value of algebraic multiplicity=1
[tex]AV=\lambda v \\& \Rightarrow A V=-V\\ \Rightarrow-V_1+V_2=-V_1\\ \Rightarrow V_2=0 \\& v_1+v_2-2 v_3=-v_3\\ \Rightarrow v_1+v_2-v_3=0\\ \Rightarrow v_1=v_3 \\[/tex]
[tex]$$\begin{aligned}& \Rightarrow \quad\left[\begin{array}{l}v_1 \\0 \\v_1\end{array}\right] \\& =v_1\left[\begin{array}{l}1 \\0 \\1\end{array}\right]\end{aligned}$$[/tex]
So, the value of eigen vectors are: [tex]& =\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right] \\[/tex]
And the value of geometric multiplicity =1
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Which statement correctly demonstrates using limits to determine a vertical asymptote of g (x) = StartFraction 2 (x + 4) squared Over x squared minus 16 EndFraction
There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = negative infinity
There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity
There is a vertical asymptote at x = –4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = negative infinity
There is a vertical asymptote at x = –4 because Limit of g (x) as x approaches 4 minus = negative infinity and limit of g (x) as x approaches 4 plus = infinity
The correct option that describes the vertical asymptote is; B: There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity
How to find the vertical asymptote of a function?A vertical asymptote of a graph is defined as a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.
A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;
In a graph, these vertical asymptotes are given by dashed vertical lines.
An example is a value of x for which the denominator of the function is 0, and the function approaches infinity for these values of x.
We are given the function;
g(x) = 2(x + 4)²/(x² - 16)
Simplifying the denominator gives;
(x² - 16) = (x + 4)(x - 4)
Thus, our function is;
g(x) = 2(x + 4)²/[(x + 4)(x - 4)]
(x + 4 ) will cancel out to give;
g(x) = 2(x + 4)/(x - 4)
Vertical asymptote:
Point in which the denominator is 0, so:
(x - 4) = 0
x = 4
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You win an online auction for a toy. Your winning bid of $30 is 60% of your maximum bid. How much more were you willing to pay for the toy than you actually paid?
Answer:
I was willing to pay $20 more for the toy than I actually paid.
Step-by-step explanation:
Let us take the maximum bid be y
So,
(y × 60) ÷ 100 = 30
60y/100 = 30
60y/100 × 100 = 30 × 100
60y = 3000
60y/60 = 3000/60
y = 50
60% of $50 is $30
So,
50 - 30 = 20
Thus, I was willing to pay $20 more for the toy than I actually paid.
which of the following commands is most likely to display the tls handshake between a client and the server at
A widely used security technology called Transport Layer Protection, or TLS, enables privacy and data security for communications over the Internet. Encrypting communication between online applications and servers, such as when web browsers load a webpage, is one of the main applications of TLS.
When a user accesses a website through HTTPS and the browser initially starts to enquire about the website's origin server, a TLS handshake occurs
Together, the client and server will perform the following during a TLS handshake:
Indicate the TLS version (TLS 1.0, 1.2, 1.3, etc.) they'll be using.
Select the cipher suites they'll employ (see list below).
Using the server's public key and the SSL certificate authority's digital signature, confirm the server's identity.
After the handshake, generate session keys to enable symmetric encryption.
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Unique buys 918 Spyder Porsche worth $845,000 every year that he owns the car
the car depreciates in value at a rate of 32% per year.
Write a function that models the value of the Porsche after t years.
*
The function for the value of the Porsche after t years is [tex]y = 845000(1-\frac{32}{100} )^t[/tex].
What is function?Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.
Given that,
The initial price of the 918 Spyder Prosche car = $845,000
Since, the price of car depreciated at the rate of 32% per year.
The function for the value of Porsche car, after t years, can be given as,
The price of car after t year is y,
[tex]y = 845000(1-\frac{32}{100} )^t[/tex]
The required function, the models, the value of the Porsche after t years is [tex]y = 845000(1-\frac{32}{100} )^t[/tex].
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Which conjecture, if any, could be made about the sum of two even integers and one odd integer?
The sum will be an even integer.
The sum will be negative.
It is not possible to make a conjecture.
The sum will be an odd integer.
The sum will be an odd integer.
What is an integer?
An integer is an integer (not a fraction) that is positive, negative, or zero.
In mathematics, integers are collections of integers and negative numbers. Like whole numbers, whole numbers do not contain fractions. Therefore, we can say that integers are numbers that can be positive, negative, or zero, but which are not fractions.
Let p,q,r be three random numbers
Let S be the sum of two even integers and one odd integer
S = 2p + 2q + (2r + 1)
S = 2p + 2q + 2r + 1
S = 2(p+q+r)+1
This shows that S is odd integer for all values of p,q,r
Therefore, the sum will be an odd integer.
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If line BG and CF are parallel,then the supplement of BIE = the supplement of GMD. Is this statement correct? Explain your answers
The supplement of BIE equals the supplement of GMD is a false assertion if lines BG and CF are parallel.
Describe the supplement angle.Angles with a supplementary sum are those whose sum is 180 degrees. For instance, the total of angle 130° and angle 50° is 180°, hence they are supplementary angles.
Lines BG and CF are parallel, as shown in the figure.
If BIE = X, then its supplement of BIE will be 180 - X;
similarly, if GMD = Y, then its supplement of GMD will be 180 - Y.
Since BG and CF are parallel, the supplements of BIE and GMD are interior angles on the same side ( as shown in figure)
and for parallel line the interior angle on the same side is 180
so 180 - X and 180 -Y there sum should be 180
They cannot be equal
line BG and CF are parallel, then the supplement of BIE = the supplement of GMD are not equal.
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Find out the missing frequency in the following incomplete distribution
CI F
0-10 3
10-20 ?
20-30 20
30-40 12
40-50 ?
The Value of median and mode are 27 and 26 respectively.
8 and 7 are missing frequency in the incomplete distribution.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Class Interval frequency Cumulative frequency
0 - 10 3 3
10 - 20 a 3+a
20 - 30 20 23+a
30 - 40 12 35+a
40 - 50 b 35+a+b
Mode = 26 hence lies in 20 - 30
f of modal class = 20
Mode = 20 + 10( 20 - a) / (20 - a + 20 - 12)
26 = 20 + 10 (20 - a) / (28 - a)
60(28 - a) = 10 ( 20 - a)
168 -6a = 200 - 10a
4a = 32
a = 8
Class Interval frequency Cumulative frequency
0 - 10 3 3
10 - 20 8 11
20 - 30 20 31
30 - 40 12 43
40 - 50 b 43+b
Median = 27
27 = 20 + 10 ( (43 + b)/2 - 11)/ 20
7 = ( (21 + b)/ 4
28 = (21 + b)
b = 7
Hence, the missing frequencies are 8 and 7.
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A biologist is studying a plant blight. At the start of their research, the blight covers a circular area with a radius of 5 kilometers. When they re-examine the blight two years later, the area has grown to a circular area with a radius of5.2kilometers. How rapidly did the radius change over the interval? _____Year/km
Step-by-step explanation:
Area of circle 1= pie r²
=3.14 x 5²
=3.14x 25
= 78.5km²
Area of circle 2=3.14 x 5.2²
= 3.14 x 27.04
= 84.9km²
change in area= 84.9-78.5
=6.4
radius²= 6.4/ 3.14
r²=2.03
r =√2.03
r=1.42
A video store manager observed that the number of DVDs sold seem to vary inversely as the price per DVD. If the store sells 710 DVDs per week when the price per DVD is $18.90, how many does he expect to sell if he lowers the price to $11.40.
If the price is reduced to $11.40 the number of DVDs sold will be 1177.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a video store manager observed that the number of DVDs sold seems to vary inversely to the price per DVD. If the store sells 710 DVDs per week when the price per DVD is $18.90.
The number of DVDs sold for $11.40 will be calculated by forming the inverse equation for the number of DVDs.
N = K / P
Here, N is the number and P is the price and K is the inverse constant.
The value of K will be,
K = N x P
K = 18.90 x 710
K = 13419
The number of DVDs for $11.40 will be,
N = K / P
N = 13419 / 11.40
N = 1177
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which of the above diagrams correctly portray a perfectly competitive firm's demand ( d) curve? a. a b. d c. b d. c
Correct option will be (C) In the short run, firms may incur economic losses or earn economic profits, but in the long run they earn normal profits.
The short run is a concept that states that, within a certain period in the future, at least one input is fixed while others are variable. In economics, it expresses the idea that an economy behaves differently depending on the length of time it has to react to certain stimuli. The short run does not refer to a specific duration of time but rather is unique to the firm, industry or economic variable being studied.
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Find the value of k given that both points lie on a line passing through the origin. (−12,−2) and (k, 8)
Using the slope, the required value of k is 48.
What is the slope?In mathematics, the steeper direction of a line is overall processed by the slope or gradient of the line.
A line's slope can be used to determine how steep it is.
Theoretically, the gradient is calculated as "rise over run" (change in y divided by change in x).
Given is a line that crosses through the origin:
y = mx
Let,s take x = -12 and y = -2.
y = mx
-2 = -12m
m = -2/12
m = -1/6
m is the slope.
The equation now:
y = mx
y = -1/6x
Now, insert:
x = k and y = 8
y = mx
8 = -1/6x
x = 6*8
x = 48
Therefore, using the slope, the required value of k is 48.
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Please hurry I have been stuck on this question for a while
One week, Heather opens a bank account with $125. Each week, starting the second week, she deposits $25 into her account.
What is the explicit rule for amount of money Heather has in her account after n weeks?
Enter the simplified answer in the box.
Answer:
125+25n
Step-by-step explanation:
We are given that
Heather opens a bank account with=$125
Each week she deposited money into her account=$25
We have to find the explicit rule for the amount of money that has Heather after n weeks.
Heather has money after 1 week=125+25=$150
Heather has money after 2 week=125+2(25)=$175
Heather has money after 3 weeks=125+3(25)=$200
Heather has money after n weeks=125+25(n)
Hence, the explicit rule for the amount of money that has Heather after n weeks is given by
125+25n
the absolute value of -7-3
negative 7 minus three
I need. Help with this question
Derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.
What is differentiation?
In arithmetic, the derivative of a function of a true variable measures the sensitivity modification of the perform price with relation to a change in its argument. Derivatives are a elementary tool of calculus.
Main body:
by using product rule;
Let = u = x² + 4x + 6
⇒ du/dx = 2x + 4 .
Now y = u⁵
⇒ dy/dx = 5u⁴ .
dy/dx = dy/dx * du/dx = 5u⁴ * (2x + 4)
= 5 * (x² + 4x + 6)⁴ * (2x + 4)
= 5(2x + 4) * (x² + 4x + 6)⁴
hence , derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.
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need the answer pls help ots
Answer:
Your answer is x = 47.
Step-by-step explanation:
First, you need to move the constant to the right-hand side and change its sign.
4x = 180 + 8
Now, you need to add the numbers.
4x = 188
Last but not least, you need to divide both sides of the equation by 4, which gets you to:
x = 47
Write an equation and solve.
When two times the difference of a number x and three is increased by five, the result is nine. What is the number?
With all this information, and reading our question carefully, we can decipher the following:
9(n-3) = 3 + (9n + 3n)
9n - 27 = 3 + (9n +3n) (Step 1. Distributive Property)
9n - 27 = 3 + 12n (Step 2. Combine like terms; 9n + 3n = 12n)
-9n -9n (Step 3. Subtract 9n from both sides to isolate the variable)
______________
-27 = 3 + 3n
-3 -3 (Step 4. Subtract 3 from both sides)
________________
-30 = 3n
----- ----
3 3 (Step 5. Divide 3 from both sides)
________________
-10 = n
Therefore, n = -10
What is Distributive property?Distributive property explains that the operation performed on numbers, available in brackets that can be distributed for each number outside the bracket. It is one of the most frequently used properties in Maths. The other two major properties are commutative and associative property.The distributive property is easy to remember. There are a number of properties in Maths which will help us to simplify not only arithmetical calculations but also the algebraic expressions. In this article, you will learn what is distributive property, formula, and solved examples.to learn more about distributive property refer to:
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Witch rate is equivalent to 15 milesper hours
Answer: 60 miles per 4 gallons. If that's the question.
Step-by-step explanation:
Which properties determine whether a quadrilateral is a parallelogram?
A. both pairs of opposite sides of a quadrilateral are both congruent and parallel
B. one pair of opposite sides of a quadrilateral is both congruent and parallel
C. it has 4 right angles
D. one pair of opposite sides of a quadrilateral is parallel
c is the answer. jdjsisiao
Out of 400 plants sold daily at a nursery, 90% of them have flowers. How many of the
plants have flowers?
A. 40
B. 90
C. 310
D. 360
10 points.
Answer: D; 360
Step-by-step explanation: To find percentages, I like to set up proportional relationships to find the amount. It would look like this:
[tex]\frac{90}{100}[/tex] = [tex]\frac{?}{400}[/tex]
90= part %
100= whole %
?= amount of the %
400= all of the item(s)
So, we would cross multiply the 90 and the 400, then divide it by 100. That would be 36,000. So, that divided by 100 leaves us with 360. I hope this helped!
A system of equations and its graph are shown.
y = 3/4x+3
y = -1/4x + 1
What is a solution to the system
Answer:
(-2, 1.5)
Step-by-step explanation:
When graphed their solution is (the point where both the line intercept/touch) (-2,1.5)
I graphed this equations online**
Use the vertex and intercepts to sketch the graph of each quadratic function give the equation of the parabola axis of symmetry use the graph to determine the function domain and range f(x)=(x-1)^2+2
The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.
Given that,
Give the equation for the parabola's axis of symmetry by sketching the graph of each quadratic function using its vertex and intercepts.
We have to determine the function domain and range using the graph is f(x) = (x-1)²+2
We know that,
Its vertex A quadratic function's form is provided by
f(x) = a(x-h)²+k
So, (h,k) is the vertex of the parabola
Take
f(x) = (x-1)²+2
(1,2) is the vertex of the parabola.
Therefore, The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.
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7. Heather used a basic fact to complete
the equation below. What is the
missing number? Explain how you
can use a basic fact to find the
missing number.
4,200 + = 700
The missing value of x = 6
What is value ?
Value in mathematics can refer to a number of closely related ideas. A mathematical value can generally be any specific mathematical object. This is most frequently a number in elementary mathematics, such as a real number like or an integer like 42.
Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value.
Values are the benchmarks or ideals by which we judge the acts, traits, possessions, or circumstances of others. Values that are embraced by many include those of beauty, honesty, justice, peace, and charity.
4200 / x = 700
If the fraction is defined, the denominator cannot equal 0:
x ≠ 0
Append the inequality as the domain:
x ≠ 0
Multiply both sides of the equation by the common denominator:
400x / x = 700 x
Reduce the fractions:
4200 = 700 x
Swap the sides:
700 x = 4200
Divide both sides of the equation by the coefficient of variable:
x = 4200 / 700
Cross out the common factor:
x = 6
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5w-15 as equivalent fraction
The required equivalent expression is given as 5(w - 3).
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
An equivalent expression of any expression is given as the simplifying the expression using various operations such as factors.
So,
Given expression,
= 5w - 15
As in the expression 5 is a common term between 5w and 15.
Take 5 commons and put the rest of the expression in the parenthesis.
= 5(w - 3)
Thus, the required expression is 5(w - 3).
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Write a function in any form that would match the graph shown below.
if the pic is blurry just zoom in!!
please need ASAPP!!!
(7x6)÷2[{45÷3(7×2-15+6)}+4)
Answer:
21/79
Step-by-step explanation:
(7x6)÷2[{45÷3(7×2-15+6)}+4)
(7*6)/2[{15(7*2-15+6)}+4)
(42)/2[{15(14-15+6)}+4)
(42)/2[{15(5))}+4)
(42)/2[{75}+4)
(42)/2[75 + 4]
(42)/2 * 79
42/2 * 79
21/79
Prove that if a ≡ b mod m and c ≡ d mod m, then ac ≡ bd mod m. [duplicate]
The four integers say a,b,c and d. If a and b are congruent to moulo m and c ,d are congruent to modulo m then ac and bd are must be congruent to modulo m .
What is congruent modulo ?Two integers a and b are "congruent modulo n" if their difference is a multiple of n or in other words we say n/(b-a) . For example, 17 and 5 are congruent modulo 3 because 17 - 5 = 12 = 4×3
We have, a ≡ b mod m => m/(a - b)
and c ≡ d mod m => m/(c-d)
Now, a + c - b - d = (a-b) + (c-d)
because, m/( a - b) and m/(c-d)
=> m/( a-b+ c-d )
=> m/(a+c)-(b+d)
=> a+c ≡ b+d mod m
We have to prove that ac ≡ bd mod m.
ac - bd = c(a-b) + b(c- d)
Now, as we see, m/(a-b) => m/c(a-b)
and m/(c-d) => m/b(c-d)
=> m/(c(a-b) + b(c-d))
=> m/(ac - bc + bc - bd)
=> m/(ac - bd)
=> ac ≡ bd mod m
Hence proved.
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1. According to the text, the three IT trends that are having the greatest impact on the IT environment are: A. Privacy management, virus suppression, and enterprise portals B. Grid computing, on-demand computing, and real-time computing C. Digital forensics, the distributed workforce, and grid computing D. Knowledge management, privacy management, and intranets E. Privacy management, enterprise warehouses, and knowledge management
Computing on demand, on the cloud, and in real time IT Enviroment is most impacted by Are is known as gird computing.
What is Data Analysis?
Data analysis is the methodical application of logical and/or statistical approaches to describe and demonstrate, summarise and assess, and assess data.
Concept:
Step 1: A network of connected computers that act as a single supercomputer to complete complex tasks like modelling or data analysis is known as gird computing.
Step 2 : On-demand computing is a delivery method in which users are provided with computing resources as needed.
Step 3 : Real-time computing refers to a computer system that responds to an event by completing a task in a predetermined amount of time. a system for air traffic management as an example.
Grid computing, on-demand computing, and real-time computing
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Solve using Substitution Method
x=4-8y
3x +24y = 12
Observing the provided equation, We can't solve these equations using substitution method or any other methods because these lines are parallel and never intersect each other.
What do you mean by equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
What is a substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
x=4-8y
3x+24=12
Taking first equation and rearranging it we get,
x+8y=4
multiply this with 3, we get 3x+24y=12 which are identical in nature. Which shows these two lines are parallel in nature. We can't solve them because parallel lines never intersect.
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Observing the provided equation, We can't solve these equations using substitution method or any other methods because these lines are parallel and never intersect each other.
What do you mean by equations?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
What is a substitution method?
The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
x=4-8y
3x+24=12
Taking first equation and rearranging it we get,
x+8y=4
multiply this with 3, we get 3x+24y=12 which are identical in nature. Which shows these two lines are parallel in nature. We can't solve them because parallel lines never intersect.
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03 Multiple Choice
Select all of the expressions that are equivalent to 2/3 (9x + 6) -1/2(8x - 4)
M. 2(x + 1)
P. 2x+6
R. 2x + 2
S. 2(x + 3)
T. 8x
Answer:
The answer is 2x + 6 or 2(x + 3)
Step-by-step explanation:
2/3 (9x + 6) -1/2(8x - 4)
(18x + 12)/3 - (8x + 4)/2
6x + 4 - 4x + 2
Rearrange it
6x - 4x + 4 + 2
Combine like terms
2x + 6
Take 2 as common
2(x + 3)
Thus, The answer is 2x + 6 or 2(x + 3)
Which set of factors corresponds to a third-degree polynomial with rational coefficients that has zeros x=2 and x=3i
(x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.
What is polynomial?
In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Main body:
as the polynomial with rational coefficients that has zeros x=2 and x=3i
(x-2) and (x-3i) are factors of third-degree polynomial.
so ,
⇒(x-2)(x-3i)
solving (x-3i)
x = 3i
squaring both sides,
x² = -9
so , (x²+9) is a factor.
hence , (x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.
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