Find all real and imaginary zeros for a polynomial function

Answers

Answer 1

For the answer to this, we turn to the all-important Fundamental Theorem of Algebra, which states that every degree-n polynomial has exactly n imaginary roots. It's important to keep in mind that this theorem doesn't tell you how to find these roots - it just tells you that they exist.

Answer 2

Final answer:

A polynomial function is an algebraic expression with one or more terms. The real zeros can be found by setting the function equal to zero and solving for x. The imaginary zeros can be found using the complex conjugate theorem.

Explanation:

A polynomial function is an algebraic expression that consists of one or more terms. The real zeros of a polynomial function are the values of x that make the function equal to zero. To find the real zeros, set the polynomial function equal to zero and solve for x using methods such as factoring, synthetic division, or the quadratic formula.

The imaginary zeros of a polynomial function are the values of x that make the function equal to a complex number. These can be found by using the complex conjugate theorem. If a + bi is a zero, then a - bi is also a zero, where a and b are real numbers and i is the imaginary unit, sqrt(-1).

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Related Questions

A rectangular prism has a length of 3/4 cubic inch and a width of 1/2 inch. The volume is 21/32 cubic inch. Find the height of the prism. Write your answer as a mixed number in simplest form.

Answers

21 / 32 = (3/4) * (1/2) * height

21 / 32 = (3 / 8) * height

21 / 32 * (3 / 8) = height =

63 / 256 inches

Answer:

[tex]\texttt{Height of the prism}=1\frac{3}{4}[/tex]

Step-by-step explanation:

Volume of rectangular prism = Length x Width x Height

[tex]\texttt{Volume of rectangular prism =}\frac{21}{32}\\\\\texttt{Length =}\frac{3}{4}\\\\\texttt{Breadth =}\frac{1}{2}[/tex]

Substituting

[tex]\frac{21}{32}=\frac{3}{4}\times \frac{1}{2}\times h\\\\h=\frac{7}{4}=\frac{4+3}{4}=1\frac{3}{4}[/tex]

[tex]\texttt{Height of the prism}=1\frac{3}{4}[/tex]

One number is 4 less than a second number. twice the second number is 19 less than 5 times the first. find the two numbers.

Answers

the answer is because i know so

The slope of the line below is –. Write a point-slope equation of the line using the coordinates of the labeled point.

A. y + 4 = 8/7 –(x + 4)
B. y – 4 = 8/7–(x – 4)
C. y – 4 = 8/7(x – 4)
D. y + 4 = 8/7(x + 4)

Answers

y - 4 = -8/7(x - 4) is the answer

Simplify 4x2(2x2− 8x + 6). 8x2− 32x + 24 6x2− 32x + 24 6 − 32x + 24x2 8x4− 32x3+ 24x2

Answers

4x^2(3x^2-8x+6)
(4*3)(x^(2+2))+(4*-8)(x^(2+1))+(4*6)(x^(2+0))
12x^4-32x^3+24x^2

1) Which statement about 5y = 2x is true?

A) The equation represents a direction variation whose consent of variations is 5/2.

B) The equation represents a direct variation whose consent of variations is 2/5.

C) The equation does not represent a direction variation.

D) The equation does not represent a line through the origin.

2) What is the equation of the graph of y = |x| shifted 3 units up?

A) y = |x| – 3

B) y = |x| + 3

C) y = |x + 3|

D) y = |x – 3|

3) Two parallel lines form an inconsistent system of equations that has no solution.

True
or
False

Answer all and Show or Explain your answer :)

Answers

1) B you can divide both sides of the equation by 5 and it will be of the form y = kx which is direct variation

2) B f(x) + k is a vertical shift up k units

3) True Because parallel lines have the same slope and different y - intercepts they do not touch thus called inconsistent. Since they do not touch they will not have a solution.

write in graphing form please! A parabola that opens down with no stretch factor that has a vertex of (-6,5)

Answers

If it has no stretch factor, then there will be no coefficient. Meaning this is a lot easier. So, we equation is

(x+6)^2 + 5

Hope this helps!

Se implicit differentiation to find an equation of the tangent line to the curve at the given point.7x2 + xy + 7y2 = 15, (1, 1) (ellipse)

Answers

F'(x, y) = 14x +xydy/dx + 14ydy/dx = 0
(xy+14y)|dy/dx = -14x
dy/dx = -14x /(xy+14y)
dy/dx |(x=1,y=1) : -14(1) / (1+14) = -14/15

using
y-y1=/x-x1 = -14/15
y-1/x-1 = -14/15
15y-15 = -14x+14
15y+14x -15-14=0
14x +15y = 29

A restaurant charges an automatic gratuity of 18% on tables with more than 6 people. A party of 8 had a bill of p. Which expression can be used to find the total cost of the meal with the gratuity?

Answers

Answer: the answer is 1.18p

Step-by-step explanation:

It is trust me (;

True or False: Is the number 2 a solution to 7≥−3k

I'm not sure about this. Please explain

Answers

It is true. If you substitute 2 in for k, then 7 is greater than or equal to -6. this statement is true because 7 is indeed greater than 6.

t is true. If you substitute 2 in for k, then 7 is greater than or equal to -6. this statement is true because 7 is indeed greater than 6.

Leena knits 10 rows in 12 min. At this pace, how long will it take her to knit the next 25 rows? Enter your answer in the box. min

Answers

Answer would be 30 mins
10 rows = 12 mins
10 rows = 12 mins
5 rows = 6 mins
----- -----
25rows 30 mins

10r=12m
5r=6m
25r=?m
25r=30m
It will take her 30 minutes to knit 25 rows

Square tiles 9-inches on a side cover the floor of a rectangular room exactly. the border tiles are white and all other tiles are blue. the room measures 18 feet by 15 feet. how many tiles are white

Answers

first convert feet to inches:
18 ft × (12in/1ft)= 216 in
15 ft × (12 in/1ft)= 180 in

divide each side of the room by 9 inches to get number of white tiles per a wall

wall 1(18ft): 216in/9in= 24 white tiles
wall 2(15ft): 180in/9in= 20 white tiles
wall 3(18ft): 216in/9in= 24 white tiles
wall 4(15ft): 180in/9in= 20 white tiles

Lastly, add up all the white tiles and subtract 4 (the tiles that we counted twice because they were the corner tiles and touched both walls)

24+20+24+20-4= 84 white tiles total

Write an equation of the line that passes through the points (−3,12) and (0,6)

An equation of the line is y=

Answers

slope = (6 - 12)/(0 +3) = -6/3 = -2

b = 6
so

An equation of the line is
y = -2x + 6

What is the best approximation for the measure of angle ABC?

Answers

cos(x) = 10.5 / 20
cos(x) = 0.525

answer
C.
x = 58.3"

Please help, this is due in 5 minutes

Answers

notice, "x" is a variable, so it varies, it will take on many values.

usually car dealers will say, you need to pay some processing fee, a flat-fee, and after that, you get charged for the "wear and tear" of the car, so by the mileage you drive, the more miles you drive, the more wear and tear, therefore, the more you pay, the less you drive, the less you pay.

0.15x <---- 15 cents for every "x", miles

if you drive 200 miles you owe 0.15(200)
300 miles the 0.15(300) and so on.

the 22, is never changing in that equation, is a constant, just like the flat-fee.

[tex]\bf \stackrel{cost}{y}=\stackrel{\textit{15c per mile}}{0.15x}+\stackrel{flat-fee}{22}[/tex]

If 3^2x+1=81, what is the value of x?

x=1/4
x=1/2
x=3/2
x=2/3

Answers

3^(2x+1)=81

3^(something)=81
3^4=81. I know this because 3X3X3X3=81
If I know 3^4=81, then I need to find a solution to get 4 for my exponent.
Let's solve.
2x+1=4
2x=3
x=3/2

What is 334.54 + 198 grams

Answers

334.54 + 198 = 532.54 grams total

hope this helps

ANSWER without rounding: 532.54 grams

Question: Is this a significant figures question?

ANSWER round to the significant figures: 533 grams

When you do addition you use the number with the least number of decimals places to determine how many decimal places will be in your answer. There are no decimal places in 198 so you would round before the decimal place in the answer (ones place).

Solve for x: −3 |x + 7| = −12

Answers

[tex]-3|x + 7|=-12\quad |:(-3)\\\\|x+7|=4\\\\\\x+7=-4\qquad\vee\qquad x+7=4\\\\x=-4-7\qquad\vee\qquad x=4-7\\\\\boxed{x=-11\qquad\vee\qquad x=-3}[/tex]

first you divide both sides by -3
then you get |x + 7| = 4
what you do now is make two separate equations
drop the absolute value signs
x + 7 = 4 OR x + 7 = -4
subtract 7 from both sides AND BOTH EQUATIONS
x = -3 OR x = -11

lets check it!

-3 |-3 + 7| = -12 -3 |-11 + 7| = -12
-3 |4| = -12 -3 |-4| = -12
-3 (4) = -12 -3 (4) = -12

yep! your answers are x = -3 OR x = -11

i hope this helps!!

Sandy bought a soft drink for 2 dollars and 6 candy bars. she spent a total of 20 dollars. how much did each candy bar cost

Answers

each candy bar was $3.00.

Find f(x) and g(x) so that the function can be described as y = f(g(x)).

y = eight divided by x squared + 2

Answers

The first thing to notice in this problem is that the math solution PEMDAS will be in effect. You will have y = 8/ (x^2 + 2) Since x isn't clarified, then there is no way to complete the solution or simplify it. This problem was worded and showed weird.

What is the square root of 53 rounded to the nearest hundreth

Answers

7.28 is the answer rounded to the nearest hundredth.
7.28010988928

What is the slope of this graph?

Answers

Since the slope is falling, instead of rising, it would be negative.

Now, on the line, I plotted (0, 2) and (-2, 10).

You would now plug this into the rise/run formula.
The formula is [tex] \frac{y2 - y1}{x2 - x1} [/tex]

The equation would become,
[tex] \frac{10 - 2}{-2 - 0} [/tex] = [tex] \frac{8}{-2} [/tex] = -4

I believe the answer would be -4.

I hope this helps!

How many 1/3 pound paperback books together weigh 25 pounds?

Answers

75 I think since 75 divided by 3 equals 25

Final answer:

We can find the quantity of 1/3 pound paperback books that weigh a total of 25 pounds by performing the calculation, 25 ÷ 1/3 or equivalently, 25 x 3, which equals 75. Therefore, we would need 75 of these books to total 25 pounds.

Explanation:

To find out how many 1/3

pound

paperback

books weigh a total of 25 pounds, we use division. Since each book weighs 1/3 of a pound, we divide the total weight we want (25 pounds) by the weight of each individual book (1/3 pound). So, our calculation would look like this:

25 ÷ 1/3

. In mathematics, dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of 1/3 is 3/1, or just 3. So, our calculation is now:

25 x 3

. Multiplying 25 by 3 gives us 75. So, we would need

of these paperback books to

weigh

a total of 25 pounds.

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Thomas paid $5 for a multicolor file folders. There were 100 folders in the box .what was the cost of each folder?

Answers

Thomas paid $5 for 100 folders, to find cost of each folder:

5/100 = $0.05

Therefore, the cost of each folder was $0.05

Hope I helped :)

5 divided by 100, since there were 100 folders n total is 5

0.05

:))

When matter changes state, what two things are always conserved?

Answers

Even though matter changes state, there are two things which are always conserved: they are mass and chemical composition. Just because the state has changed, it does not mean that any new molecules are either created or have been destroyed. The Law of Conservation of mass explains this concept.

In a change of state, mass and energy are the two things that are always conserved, in accordance with the law of conservation of matter and the first law of thermodynamics, respectively.

When matter changes state, the two things that are always conserved are mass and energy. This is explained by the law of conservation of matter, which states that the total mass of the products must equal the total mass of the reactants in a chemical reaction, and the law of conservation of energy, often referred to as the first law of thermodynamics.

In any given closed system, neither mass nor energy is created or destroyed, but can be transformed from one form to another. For example, when a substance burns, its matter is not lost but is instead transformed into other substances with the same total mass. Likewise, energy can be moved or transformed, but the total amount of energy remains constant. These principles apply to both living and non-living systems, keeping the total quantity of matter and energy fixed in the universe.

A right triangle has one angle that mesures 23. The adjacent leg measures 27.6 cm and the hypotenuse measures 30cm.

What is the approximate area of triangle? Round to the nearest tenth

Area of the triangle =1/2bh

A:68.7cm^2
B.161.7cm^2
c.381.3cm^2
D450.cm^2

Answers

you can start by finding the height or altitude ("alt" = vertical side touching hypotenuse and bottom base):
tangent (23) = opposite/adjacent (TOA), where opposite is altitude and adjacent is base
So tangent (23) = alt/27.6cm
alt = 27.6×tan23 = 27.6×0.424
alt = 11.72cm
So now area = 1/2 (b)(h), where h=alt
area = 1/2 (27.6cm)(11.72cm) = 161.7cm^2
[tex] 161.7{cm}^{2} [/tex]
So the correct answer is [B.]

The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s. when the length is 20 cm and the width is 10cm, how fast is the area of the rectangle increasing

Answers

Let l = length of the rectangle,
b = breadth of the rectangle,
a = area of the rectangle,
t = time,

So, [tex] \frac{dl}{dt} [/tex] = 8 cm/s &
[tex] \frac{dw}{dt} [/tex] = 3 cm/s

Area of the rectangle, a = l × w

Differentiate the equation with respect to t,

[tex] \frac{da}{dt} [/tex] = l × [tex] \frac{dw}{dt} [/tex] + w × [tex] \frac{dl}{dt} [/tex]

[tex] \frac{da}{dt} [/tex] = 20 × 3 + 10 × 8

[tex] \frac{da}{dt} [/tex] = 60 + 80

[tex] \frac{da}{dt} [/tex] = 140 [tex] cm^{2} [/tex]/s

Therefore, the correct answer is 140 [tex] cm^{2} [/tex]/s.

The information that is given:
dl/dt = 8 (rate of length increasing)
dw/dt = 3 (rate of width increasing)
l = 20 (when the length is 20)
w = 10 (when the width is 10)

The unknown is dA/dt (the rate the area is increasing)

Start with the formula for the area of a rectangle
A = w*l
Find the derivative of it
d/dt(A) = d/dt(w*l) Use the multiplication rule
dA/dt = w(dl/dt) + l(dw/dt)
Substitute in what is known from above
dA/dt = 10(8) + 20(3) = 80+60 = 140
The area is increasing 140 square centimeters per second

PLEASE HELP!!! Will give brainliest!

Answers

The correct answer would be 24, I don't know how to show the work but you can go on youtube.

Hope this helps!

A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak.

Answers

Hey there!

A= value of the first term
n= the number of the term you want to find
r= common ratio
value of r is = 2/3 because 27 times 2/3 = 18 which is the second term
n = 4 since you want to find the 4th term in the sequence
Plug it in and results are
4th term = 27(2/3)^(4-1) = 8
The answer is 8

Hope this helps!

A sequence can be used to illustrate the difference in heights of each jump and develop a pattern from them. In this case, we have 27, 18, 12,... Assuming the pattern continues, we have the previous height divided by 3 and then subtracted from itself:
[tex]a_n=a_{n-1}-\frac{a_{n-1}}{3}[/tex]

Here:
[tex]a_4=a_3-\frac{a_3}{3}=12-\frac{12}{3}=12-4=8[/tex]

Solve for x. 5x−2(x+1)=1/4

Answers

5x - 2(x+1) = 0.25

5x - 2x + 2 = 0.25

3x = 0.25 - 2

3x/3 = -1.75/3

x = - 0.583

hope this helps

5x - 2(x+1) = 0.25

5x - 2x + 2 = 0.25

3x = 0.25 - 2

3x/3 = -1.75/3

x = - 0.583
yes ik i copied but points are worth more than integrity

How to write three times the difference of two times m and five is equal to eight times m to the second power increased by four in a problem?

Answers

you would have to do 14 promblems'

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