Form a third-degree polynomial function with real coefficients, with leading coefficient 1, such that - 2 + i and 7 are zeros.

Answers

Answer 1

In standard form, this third-order polynomial - call it p(x) - has real coefficients a, b, c, d so that it is written as

p(x) = a x ³ + b x ² + c x + d

We're told the leading coefficient is a = 1, so

p(x) = x ³ + b x ² + c x + d

Since the coefficients are all real, any complex roots with non-zero imaginary part occurs alongside its complex conjugate, so the fact that -2 + i is a root means that its conjugate, -2 - i is also a root.

Then by the factor theorem, we can write p(x) as the product of linear terms involving its roots:

p(x) = (x - (-2 + i )) (x - (-2 - i )) (x - 7)

Now just expand this to get

p(x) = x ³ - 3 x ² - 23 x - 35


Related Questions

What is the answer to 6% of 19.5?

Answers

Answer:

1.17

Step-by-step explanation:

Charlie's car can travel 40 miles using 2 gallons of gas.
At this rate, how far, in miles, can Charlie travel using 7.6 gallons of gas?
2

Answers

Answer:

152 miles

Step-by-step explanation:

Ratios:

[tex]\frac{40}{2} =\frac{x}{7.6} \\\\2x=304\\x=152[/tex]

Which equation is graphed in the
coordinate plane?
a. f(x) = (x + 3)2 - 5
b. f(x) = -(x + 3)2 – 5
c. f(x) = (x - 3)2 - 5
d. f(x) = -(x - 3)2 – 5
HELP PLEASE

Answers

Answer:

do u have calculator?

Step-by-step explanation:

u need to put that equations in the graph

Answer:

y = -(x + 3)^2 - 5 (this is Answer b)

Step-by-step explanation:

Identify the coordinates of the vertex (h, k) by looking at the graph:  the x-coordinate, h, is -3 and the y-coordinate is -5.  The graph opens down, so the function begins with a negative sign:  y = -(x + 3)^2 - 5 (this is Answer b).

What is the answer the pie

Answers

Answer:

3.14159265359 and so on

Step-by-step explanation:

What is the area of the following circle?
r = 4

Answers

Answer:

The area of this circle is 50.27

Step-by-step explanation:

The area of this circle is 50.3 units² or 16π

What is incircle?

The incircle is defined as the largest circle that can be made in a triangle and is tangent to each side of the triangle.

The area of the circle is the product of the pie and the square of the radius.

The area of the circle = πr²

We are given that radius of the circle as r = 4.

Then we know that

Area = πr²

Substitute the values r = 4

π = 3.14

Area = 3.14(4)²

Area = 3.14 × 16

Area = 50.3

Learn more about the area;

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I NEED HELP PLS!! it shouldnt be too hard bc im in 6th grade

Answers

Answer:

2x + 1

Step-by-step explanation:

That person added everything together that was shown which is incorrect. You shouldn't add the 12x + 3 as that should be the end result. You add 3x + 3x + 4x + 2 to get 10x + 2. You then subtract that by 12x +3 which is 2x + 1

What is the volume of a sphere that has a diameter of 12 cm? (Round to the nearest whole number)

Answers

Answer:

V≈904.78cm³

Step-by-step explanation:

PLS HELP I HAVE 5 MIN

Answers

Answer:

? where's the question

Step-by-step explanation:

What is the equation of a circle that has a diameter of 10 units if its center is at (3,8)?

Answers

Answer:

Step-by-step explanation:

[tex](x-3)^2+(y-8)^2 = 25[/tex]

The equation of circle: (x - 3)² + (y - 8)² = 25

What is equation of circle?

An equation of circle with center (h, k) and radius 'r' is,

(x - h)² + (y - k)² = r²

For given example,

a diameter of circle = 10 units

So, the radius would be (r) = 10/2

r = 5 units

And the center (h, k) = (3, 8)

So, the equation of the circle would be,

⇒ (x - 3)² + (y - 8)² = 5²

⇒ (x - 3)² + (y - 8)² = 25

Therefore, the equation of circle: (x - 3)² + (y - 8)² = 25

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Mark is going to an awards dinner and wants to dress appropriately. He had one blue shirt, one white dress shirt, one black dress shirt, one pair of black slacks, one pair of grey slacks, and one red tie. All six of marks possible outfits are listed below

Answers

Answer:

All the four statements are true , which are -

(A) The subset contains contains of all the outfits that have grey slacks .

(B)  The subset contains contains of all the outfits that have grey slacks and red tie .

(C) The subset contains contains of all the outfits that have grey slacks and blue shirt .

(D)  The subset contains contains of all the outfits that do not have black slacks .

Step-by-step explanation:

We are given with Outfit 2 , 4 and 6

Outfit 2 -   Blue     grey     red

Outfit 4 -   White    grey     red

Outfit 6   - Black     grey    red

(A) Since only 2,4, and 6 contain grey slacks, and no other outfit contains grey slacks, those are the subsets that contain grey slacks. Thus , this statement is true .

(B) Just outfits 2, 4, and 6 have grey slacks and a red tie, proving the statement. Other clothes do not include grey slacks and a red tie; they may include a red tie but not both grey slacks and a red tie. Hence , the statement is true .

(C) Since the outfit 2 has grey slacks and a blue shirt, the statement is correct; no other outfit has both grey slacks and a blue shirt. Therefore , this statement is also correct .

(D) The argument is correct since all of the subsets contain grey slacks and no black slacks.

Hence , all the options A , B , C , D are correct and describes the subset .

The given question is incomplete , the complete question is attached here -

Can you please help me I need help asap thanks

Answers

Answer:

36

Step-by-step explanation:

the answer to the question is 36

A teacher calculated the mean of 27 students mark to be 62. A student who later completed the assessment got a mark of 53. What is the new mean of the class, to two decimal places?

Answers

Answer:

first of all the average score of students is 62.

and there are 27 students

so full marks scored by students are 27×62= 1674

and 1 new students added to that so his score would be 1674+ 53(his marks)= 1727

so now the mean of students are beause there are one more students so 27+1 = 28 then 28÷1727= 61.6 is the mean now

Pleas help! I will give brainliest to the first answer!

Answers

Answer:

hi

Step-by-step explanation:

Help with what where is the picture or your answer lol?

Connor invests $1,400 in a savings account that increases annually at a 9% interest rate. Determine how much money Connor will have after 4 years. Round to the nearest cent.

Answers

Answer:

$1,976.21

Step-by-step explanation:

$1,976.21

एउटा झोलामा 15 ओटा असल र 5 ओटा खराब स्याउहरू
छन् । तीमध्ये दुईओटा स्याउहरूलाई पुन: नराखीकन निकाल्दा
बन्ने सम्भावित परिणामहरूको सबै सम्भाव्यताहरूलाई
वृक्षचित्रमा देखाउनुहोस्।​

Answers

Answer:

15 apples good

5apples bad

answer 5

Please answer correctly! I will mark you Brainleist!

Answers

Answer:

72 cm^3

Step-by-step explanation:

The volume of a rectangular prism is the length x width x height, so

6*3*4=72

72 is the answer have a nice day

100 students participate in sport or music.60 participate in sports and 50 participate in music. How many students participate in both activities?Using Venn-diagram,find the number of students who participate only in music.​(help me)

Answers

Answer:

40 students participate only in music.

Step-by-step explanation:

When you add the two groups together, you get 50 + 60 = 110.  But there are only 100 students, so 10 of them must have been counted twice (they do music AND sports.  Put 10 in the middle part of the Venn diagram (image2).

Subtract 10 from each of the two groups to find the number of students taking only one of the two subjects.  For example, there are 50 music students, but 10 of them also do sports, so 50 - 10 = 40 students do only music.  (There are 60 - 10 = 50 students who participate only in sports.) (image3).

Can someone, anyone, help me with this?

Answers

here’s the answer sorry if it’s hard to read

la respuesta de tu potencia es 1

(I BEG YOU HELP ME TUTORS! ITS A MULTIPLE CHOICE ILL GIVE U BRAINLY)

Answers

Answer:

ans= (2)

Step-by-step explanation:

y=x²-1 is the only quadratic function there

1 is a linear function

3 is a cubic function

4 is a a constant function

need help im struggling ​

Answers

Answer:

undefined

Step-by-step explanation:

sorry if it's wrong

Answer:

answer is zero

Step-by-step explanation:

Given what you have learned about inverse functions, what can you say about the functions y = 2^x and y = log 2 X.

Answers

Answer:

[tex] log(2x) = {2}^{x} \\ ln \: \times log = ln( {2}^{x} ) \\ 1 = x ln(2) \\ x = \frac{1}{ ln(2) } [/tex]

Graph each equation using slope intercept form y = x + 6

Answers

Answer: The graph of the equation y = x + 6 looks like this! (see attached screenshot)

Step-by-step explanation:

I graphed using Desmos, an online graphing calculator.

The graph of the linear function y = x + 6 is attached below showing a

y - intercept of 6.

What is graph of a linear equation?

The graph of a linear equation is a straight line on a Cartesian coordinate system. A linear equation can be represented in the form       y = mx + b, where m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis).

The graph of a linear equation can have different orientations and slopes, depending on the values of m and b. It can be upward-sloping (positive slope), downward-sloping (negative slope), or horizontal (slope of 0). The steepness of the line is determined by the magnitude of the slope.

Using a graphing calculator, the slope of the equation is 1 and the y-intercept is 6.

Learn more on graph of a linear equation here;

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Resolver las siguientes inecuaciones cuadráticas y presentar el conjunto solución en forma de intervalo y gráficamente. 1) X2 < 10 – 3x 2) 2x2 + 3x ≥ 2

Answers

Respuesta:

1) (-5,2)

2) [tex](-\infty,-2]U(\frac{1}{2},\infty)[/tex]

Explicación paso a paso:

1)

[tex]x^{2}<10-3x[/tex]

Para comenzar este problema, debemos moverlo todo al lado izquierdo de la inecuación, por lo que obtenemos:

[tex]x^{2}+3x-10<0[/tex]

Ahora podemos factorizar el lado izquierdo para obtener:

[tex](x+5)(x-2)<0[/tex]

Ahora podemos cambiar el símbolo < por un = para encontrar los valores de x en los cuales la inecuación es igual a cero.

(x+5)(x-2)=0

Y luego despejamos x.

x+5=0

x=-5

y

x-2=0

x=2

Ahora construimos nuestros intervalos posibles.

[tex](-\infty,-5)[/tex]

(-5,2)

y

[tex](2,\infty)[/tex]

Y escogemos algunos valores de prueba. Estos nos ayudarán a determinar si cada intervalo hace que la inecuación sea verdadera o falsa.

[tex](-\infty,-5)[/tex]

Para este intervalo escojamos -6 y evaluemoslo en la inecuación.

(x+5)(x-2)<0

(-6+5)(-6-2)<0

(-1)(-8)<0

8<0

falso, así que este intervalo no es parte de nuestra respuesta.

(-5,2)

para este escojamos x=0 y probémoslo en la inecuación.

(x+5)(x-2)<0

(0+5)(0-2)<0

(5)(-2)<0

-10<0

verdadero, así que este intervalo es parte de nuestra respuesta.

[tex](2,\infty)[/tex]

Para este escojamos 3 y probémoslo en unestra inecuación.

(x+5)(x-2)<0

(3+5)(3-2)<0

(8)(1)<0

8<0

falso, así que este intervalo no es parte de nuestra respuesta.

así que nuestra respuesta es:  (-5,2)

Vea imagen adjunta para representación gráfica.

2)

[tex]2x^{2}+3x\geq2[/tex]

Para resolver este problema, comenzamos moviéndolo todo al lado izquierdo de la inecuación.

[tex]2x^{2}+3x-2\geq0[/tex]

Ahora podemos factorizar el lado izquierdo de la inecuación para obtener:

[tex](2x-1)(x+2)\geq0[/tex]

Ahora podemos cambién el símbolo ≥ por un símbolop de = para obtener los valores de x que hacen que la inecuación sea igual a 0.

(2x-1)(x+2)=0

y ahora despejamos x.

2x-1=0

[tex]x=\frac{1}{2}[/tex]

y

x+2=0

x=-2

Ahora construimos nuestros intervalos posible.

[tex](-\infty,-2][/tex]

[tex][-2,\frac{1}{2}][/tex]

y

[tex][\frac{1}{2},\infty)[/tex]

Ahora escogemos los valores de prueba correspondientes.

[tex](-\infty,-2][/tex]

para este, escojamos -3 y probémoslo en la inecuación.

[tex](2x-1)(x+2)\geq0[/tex]

[tex](2(-3)-1)(-3+2)\geq0[/tex]

[tex](-7)(-1)\geq0[/tex]

[tex]7\geq0[/tex]

verdadero, así que este intervalo es parte de nuestra respuesta.

[tex][-2,\frac{1}{2}][/tex]

para este, utilicemos 0 como valor de prueba.

[tex](2x-1)(x+2)\geq0[/tex]

[tex](2(0)-1)(0+2)\geq0[/tex]

[tex](-1)(2)\geq0[/tex]

[tex]-2\geq0[/tex]

falso, así que este intervalo no es parte de nuestra respuesta.

[tex][\frac{1}{2},\infty)[/tex]

para este, utilicemos 1 como valor de prueba.

[tex](2x-1)(x+2)\geq0[/tex]

[tex](2(1)-1)(1+2)\geq0[/tex]

[tex](1)(3)\geq0[/tex]

[tex]3\geq0[/tex]

verdadero, así que este intervalo es parte de nuestra respuesta.

Así que nuestra respuesta es la unión entre los dos intervalos que resultaron verdadero, por lo que nuestra respuesta es:

[tex](-\infty,-2]U[\frac{1}{2},\infty)[/tex]

Vea la representación gráfica en la imagen adjunta.

The figure is composed of a right triangle inside a rectangle

Answers

Answer:

there is no figure

Step-by-step explanation:

a train travels a distance of 1000m along a track. find the work done by the train by applying a force of 15000​

Answers

Answer:

1000 meters

Step-by-step explanation:

is this proportional or non-proportional?

Answers

Answer:

yes it is porportional!

Step-by-step explanation:

Because if you divide the y values by their own x value you will always get the same number which is 12. Meaning that, that is the constant.

Select the correct answer.
What is the difference of the values of the two variables in this system of equations?
y= 2x+1
x + 3y = 10

A. 0
B. 1
C. 2
D. 3​

Answers

The Answer is choice C

Proteins can transport other substances to wherever they are needed in the body.
TRUE
FALSE

Answers

False because jrirjtjtjtjtjtjtjjtjtjfjfjjrjrjtktktkfkrkkrktktk

Answer:

proteints hi where they need to go body

8 + 6 x 9

More about to come

Answers

Answer:

62

Step-by-step explanation:

8+(6*9)

8+54

62

8 + 6 x 9 = 62

hope this helps

Please help me out with this no links and not stealing points

Answers

Answer: The sum of the number of angles in a polygon is (n-2) * 180, where n is the number of sides, so the sum of the angles of a  17-sided polygon is (17-2) * 180 = 2700.

Step-by-step explanation:

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