Two roots of a third degree polynomial function f(x) are -4 and 4. Which statement describes the number and nature of all
roots for this function?
* f(x) has three imaginary roots.
* f(x) has three real roots.
* f(x) has two real roots and two imaginary roots.
* f(x) has three real roots and one imaginary root.
Answers
Answer:
f(x) has three real roots.
Step-by-step explanation:
f(x) has three real roots.
A third degree polynomial function with real coefficients has exactly 3 roots.
Furthermore, all complex roots come in pairs, either there is none, or there are exactly two conjugates, which are in the form e1+i(e2) and e1-i(e2) where e1 and e2 are polynomial expressions.
This also means that a third degree polynomial with real coefficients has at least one real root, or three.
Since we are given two real roots for the given polynomial, the third root cannot be complex alone, so the only possibility is that there are three real roots.
If b is real, then all three roots are real.
If b is not real, then two of the roots are real (-4 and 4) and one is imaginary.
What is a polynomial?Polynomial is an equation written with terms of the form kx^n.
where k and n are positive integers.
There are quadratic polynomials and cubic polynomials.
Example:
2x³ + 4x² + 4x + 9 is a cubic polynomial.
4x² + 7x + 8 is a quadratic polynomial.
We have,
The polynomial function f(x) has degree 3 and two roots -4 and 4, we know that (x + 4) and (x - 4) are factors of the function.
To see why, note that when x = -4, the factor (x + 4) becomes zero, making the function zero.
Similarly, when x = 4, the factor (x - 4) becomes zero, making the function zero.
Now,
Since the function has degree 3 and two factors of degree 1, we can conclude that the third factor is also of degree 1.
This means that the function can be written in the form:
f(x) = a (x + 4) (x - 4) (x - b)
where a and b are constants.
We don't know the value of b, but we know that it is a real number (since the other two roots are real).
Thus, the three roots of the function are -4, 4, and b.
Now,
To determine whether the roots are all real or some are imaginary, we need to know the value of b.
If b is real, then all three roots are real.
If b is not real, then two of the roots are real (-4 and 4) and one is imaginary (b).
Thus,
If b is real, then all three roots are real.
If b is not real, then two of the roots are real (-4 and 4) and one is imaginary.
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Related Questions
Help me with this really fast
Answers
Answer:
quadratic trinomial ..........................
Plz send the Venn diagram of this...
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Answer:
Step-by-step explanation:
sorry im not sure
Granite has a specific heat of 800 J/g oC. What mass of granite is needed to store 150,000 J of heat if the temperature of the granite changes from 80 oC to 95 oC? (12.5 g)
Answers
Answer:
12.5g
Step-by-step explanation:
Given data
Shc= 800 J/g oC
Q=150000J
T1= 80
T2= 95
Q=mc(T2-T1)
150000= m*800(95-80)
150000= m*800*15
150000= 12000m
m= 150000/12000
m= 12.5g
Find the volume of the sphere. Round your answer to the nearest tenth.
Answers
Answer:
B..................................
Answer:
below
Step-by-step explanation:
v of sphere
v = 4/3 πr³
v= 4/3 *3.142*10³
v = 4188.8cm³
..... B is correct
Suppose g(m) varies inversely with M and g (m) = 3.5 when m = 10.
What is the value of m when g (m) = 5 ?
Answers
Answer:
m =7.
Step-by-step explanation:
Let the constant number = k.
g(m) = k/m,
3.5 = k/10,
k = 35.
Thus, when g(m) = 5 = 35/m, m = 7.
Find the perimeter of a rectangular strip of board is 3.28m long and 7.5m
Answers
Answer:
21.56 m
Step-by-step explanation:
2(3.28) + 2(7.5)
(twos represent the sides)
6.56 + 15
= 21.56 m
m: 4,y-intercept: -3
Answers
Answer:
気わぴてぽ場来委ノヤセケ営非イソ坊管るゅぐ始属度ナ作78円レ話1既オ穫橋サエノス高境ド紀健ヨ出球用知ドルぐし。一ぞレゃ者5縮に策初ホムユス就張ヘ例芸んばれ予定ウホ所物メヤマ布事3者フリ京著ユ月遠ぐ円晶郊せはル。案馬がみわ員連じへい液済そ伝深優アネソ問合都フび渡格ンにづだ人配7初クエ縮杉ラマハ干照く漁更保間す辞表メフナヒ辞発だょより軍綱てかで線説般郎彩そン。
Step-by-step explanation:
気わぴてぽ場来委ノヤセケ営非イソ坊管るゅぐ始属度ナ作78円レ話1既オ穫橋サエノス高境ド紀健ヨ出球用知ドルぐし。一ぞレゃ者5縮に策初ホムユス就張ヘ例芸んばれ予定ウホ所物メヤマ布事3者フリ京著ユ月遠ぐ円晶郊せはル。案馬がみわ員連じへい液済そ伝深優アネソ問合都フび渡格ンにづだ人配7初クエ縮杉ラマハ干照く漁更保間す辞表メフナヒ辞発だょより軍綱てかで線説般郎彩そン。
y=4x–3
y-y1=m(x-x1)
y+3=4(x-0)
y+3=4x-0
y+3=4x
y=4x-3
LCM of the given set of counting numbers 45,20,10
Answers
Evaluate the function.
f(x) = -x2 + 6x + 4
Find f(-7)
PLSS HELP TODAY IS THE LAST DAY
Answers
Answer:
-87
Step-by-step explanation:
-(-7^2) + 6(-7) + 4
-49 -42 + 4
-87
Answer:
f(-7) = -3
Step-by-step explanation:
The exponentiation x^2 must be done before multiplication by the coefficient -1.
Substituting -7 for x, we get:
-(-7)^2 + 6(-7) + 4 = f(-7)
Then f(-7) = -49 + 42 + 4, or
f(-7) = -3
Factorize (2ax-2ay-3by+3bx)
Answers
Answer:
That's the answer I searched for and I hope it can help.
#Carryonlearning
Please make me brainliest!
Three boards are placed end to end to make a walkway. The first board is 4 feet 5 inches long, the second board is 6 feet 9 inches long,and the third board is 3 feet 11 inches long. How long is the walkway?
Answers
Answer:
15 feet and 1 inch long
Step-by-step explanation:
add up the feet: 4+6+3= 13 feet
add up the inches: 5+9+11 = 25 inches
25/12= 2 feet 1 inch
13 feet + 2 feet + 1 inch= 15 feet 1 inch
Plz help i need a correct answer asap
Answers
A is
[tex] | - 9| + |9| [/tex]
absolute value is always positive, the minus sign vanishes (it literally means "how far away from zero" something is. distance can't be negative.)
B ist just 18
Andy is comparing how long two tablets can be used after being fully charged.
-
Tablet A Tablet B
(minutes) (minutes)
540
593
Mean
Median
580
589
NOR
21
13
MAD
6
2
Answers
Answer:
Part A: On average Tablet B's battery will last longer.
Part B: The MAD is lower in tablet B's battery life so Tablet B is more consistent.
Step-by-step explanation:
What is the volume of this figure?
Answers
Answer:
[tex]volume = 4 \times 4 \times 4 \\ = {4}^{3} \\ = 64 \: cubic \: ft[/tex]
A ladder 18 ft long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ = π 3 ?
Answers
Answer: [tex]9\ ft/rad[/tex]
Step-by-step explanation:
Given
Length of the ladder is [tex]l=18\ ft[/tex]
Angle between the wall and the ladder is [tex]\theta[/tex]
from the figure, we can write
[tex]\Rightarrow \sin \theta=\dfrac{x}{18}\\\\\Rightarrow x=18\sin \theta[/tex]
Differentiate the above equation w.r.t [tex]\theta[/tex]
[tex]\Rightarrow \dfrac{dx}{d\theta}=18\cos \theta\\\\\text{at }\theta=\dfrac{\pi }{3}\\\\\Rightarrow \dfrac{dx}{d\theta}=18\cos(\dfrac{\pi}{3})\\\\\Rightarrow \dfrac{dx}{d\theta}=18\times 0.5\\\\\Rightarrow \dfrac{dx}{d\theta}=9\ ft/rad[/tex]
Madelyn needs to order some new supplies for the restaurant where she works. The restaurant needs at least 518 glasses. There are currently 314 glasses. If each set on sale contains 8 glasses, which inequality can be used to determine s, the minimum number of sets of glasses Madelyn should buy? Submit Answer 518 < 8(314 + 8) O 518 > 8(314+ s) O 314 +8s < 518 314 +8s > 518
Answers
Answer:
(D)
314 + 8s >= 518
Step-by-step explanation:
Answer: 314 + 8s ≥ 518
kelly wants to make a box in the shape of a cube.How many pieces of wood does she need? In what shape should she cut them?
Answers
What is the slope of the line below
Answers
Answer:
D. 1/2
Step-by-step explanation:
Step-by-step explanation:
The answer is 1/2. As the slop means gradient. so Gradient = change in Y / change in X .
calculate the following range of scores for a continuous variable: 9,8,7,6,5,4,3,2. Use upper and lower real limits to calculate your answer.
Answers
Answer:
7
Step-by-step explanation:
Given the data :
9,8,7,6,5,4,3,2
Ordering the data from least to highest :
2, 3, 4, 5, 6, 7, 8, 9
The range of a dataset is given by :
Maximum - Minimum
Maximum value = 9
Minimum value = 2
Range of data:
9 - 2 = 7
Range = 7
What is the scale factor from Figure A to Figure B? (Please help)
Answers
Answer:
3
Step-by-step explanation:
You can look at the left side of figure thred, it’s one, and b’s left side is 3. To find the scale factor, you divide the second figure by the first. So 3/1=3
Which expression represents the probability of choosing an item from the intersection of A and B
Answers
OPTION A is the correct answer
The intersection of event A and B is given by P( A∩B) , Option A is the correct answer.
What is Probability ?Probability is the likeliness of an event to happen.
It is given that the Probability of two independent event A and B is given by
P(A) and P(B)
The intersection of event A and B is given by
P( A∩B)
Therefore Option A is the correct answer.
To know more about Probability
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To bill customers for water usage, one city converts the number of gallons used into units. This relationship is represented by the equation u = 748g, where g is the total number of gallons of water used and u is the number of units.
Determine which statements about the relationship are true. Choose two options.
g is the dependent variable.
u is the dependent variable.
g is the independent variable.
u is the independent variable.
The two variables cannot be labeled as independent or dependent without a table of values.
Answers
Answer: u is the dependent variable
g is the independent variable
Step-by-step explanation:
Based on the relationship, represented by the equation u = 748g, where g is the total number of gallons of water used and u is the number of units, then :
u is the dependent variableg is the independent variableWhat are the independent variables and dependent variable?An independent variable serves as the variable that one can manipulate then control, an experimental so one can actually record the effects.
Independent variable on the other hand serves as the cause which have an independent values compare to others.
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The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between and minutes. Find the probability that a randomly selected passenger has a waiting time minutes.
Answers
Answer:
Incomplete question, but I gave you a guide on the uniform distribution, and thus you just have to replace the values in these equations to find the desired probabilities.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{a - x}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Between a and b minutes.
Here you get a and b for the uniform distribution.
Find the probability that a randomly selected passenger has a waiting time minutes.
Here you will have the value of x.
4. Find the circumference of the circle. Use 3.14 for the value of x. Round your answer to the nearest tenth.
20 in
Answers
Answer:
18.2cm
thank you
i think
(don’t mind me just trying to get my points up)
If x = 3k + 2 and y = k - 2 is a solution of linear equation 5x - 3y = 4 , then the value of k
pls can say the answer fast
Answers
5(3k+2)-3(k-2)=4
15k+10-3k+6=4
12k+16=4
12k=4-16
K=-12/12
K= -1
Find the length of the third side. If necessary, round to the nearest tenth.
Answers
Answer: 14.4
Step-by-step explanation:
PLEASE HELP ME!!!!
QUESTION WILL BE WORTH 10 POINTS!!!
I WILL MARK BRAINLIEST!!!!
Please answer the 3 questions on the picture.
I would appreciate it so much.
Answers
Answer:
lol i dont know but yo dog smell like evolution and natural selection?
Step-by-step explanation:
Answer:
11.) 180-38=142 12.)24.5 13.)im not sure but want to say 10
Step-by-step explanation:
On a piece of paper, graph f(x)=16x0.5^x. Then determine which answer choice matches the graph you drew.
Answers
9514 1404 393
Answer:
A
Step-by-step explanation:
You can use x=0 and x=1 to find points that must be on the graph.
f(0) = 16·0.5^0 = 16
f(1) = 16·0.5^1 = 8
Only graph A matches these points.
1. For each of 200 randomly selected cities, Gary recorded the number of churches
in the city (x) and the number of homicides in the past decade (y). He calculated
the linear correlation coefficient and was surprised to find a strong positive linear
correlation for the two variables. Does this suggest that building new churches
causes an increase in the number of homicides? Why do you think that a strong
positive linear correlation coefficient was obtained? Explain your answer with
reference to the term lurking variable.
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
When certain variables are examined, there seems to be a sort of spurious relatuoshipnornassocuation between the two variables, this is evident in the relationship between churches and the number of homicide, when a strong positive correlation is observed between number of churches and number of homicides, this relationship is most likely to be due to the effect of a lurking or third variable which creeped into our analysis, a factor which has a posithe correlation on both number of churches and homicide level, Number of homicide and number of churches could have been correlated by the lncreasing population which may lead to overcrowding and competition Hence increasing rate of homicide, similarly, with high rise in population, the growth of church to accommodate the populees will also creep in.
Paul bakes raisin bars in a pan shaped like a rectangular prism. The volume of the pan is 480 cubic inches. The
HURRY PLEASE
length of the pan is
12 inches, and its width is 10 inches
V = 480 in^3
h = ?
12 in
10 in
What is the height of the pan?
Enter your answer in the box
in inches
Answers
Answer:
The height of the pan is 4 in.
Step-by-step explanation: