For the equation, 2x^4 -5x^3+10=0 find the number of complex roots and the possible number of real roots.
A. 3 complex roots; 0, 2 or 4 real roots
B. 3 complex roots; 1 or 3 real roots
C. 4 complex roots; 0, 2 or 4 real roots
D. 4 complex roots; 1 or 3 real roots

Answers

Answer 1
The given equation is
2x⁴ - 5x³ + 10 = 0

Because this is a 4th degree polynomial, there are 4 possible real and complex roots.

Let f(x) = 2x⁴ - 5x³ + 10
Apply Descartes' Rule of signs.
There are 2 sign changes, so there are 2 possible positive real roots.

f(-x) = 2x⁴ + 5x³ + 10
There are no sign changes, so there are no negative real roots.

This means that
(a) There are possibly 2 real positive roots, and a conjugate pair of  2 complex roots;
(b) 0 real roots, and 2 pairs of 4 complex roots.

Of the given answers, only C. can be correct.
Note that complex roots always occur as conjugate pairs, so A and B are incorrect.

Answer: C
4 complex roots; 0, 2, or 4 real roots

Related Questions

What is 1 more ten than 11?

Answers

 one  more ten than 11 is 21

your answer is 21

hope this helps

Tom jogged 3/5 mile on Monday and 2/6 mile on Tuesday how much farther did Tom joy on Monday then on Tuesday

Answers

[tex]\bf \cfrac{3}{5}-\cfrac{2}{6}\impliedby \textit{so, we'll use an LCD of 30}\implies \cfrac{(6\cdot 3)-(5\cdot 2)}{30} \\\\\\ \cfrac{18-10}{20}\implies \cfrac{8}{20}\implies \cfrac{2}{5}[/tex]

For rhombus LMNO, m∠LON = 102° and NP = 5 units. Use the diagram of rhombus LMNO to find the missing measures. The measure of ∠LPM is °. The measure of ∠PMN is °. The length of LN is units.

Answers

LPM = 90

PMN = 51

LN = 10

Answer:

1. 90

2. 50

3. 10

Step-by-step explanation:

The pie below is cut into 6 equal slices. Show shade 2/3 of this pie.

Answers

Shade 4 slices out of the pie
In order to do this....

Just shade 4 out of 6 slices.

This is because 2/3 = 4/6.

To be sure you can even simplify 4/6 to 2/3.

Hope this helps!

99 POINTS POSSIBLE!!!! I have a lot of math problems.....Please show your work also:) I will give Brainiest too!

1.Chase picked three buckets of blackberries that weigh: 2.79 pounds, 2.45 pounds, and 2.62 pounds. What is the average weight for the three buckets?

2. Ashley is baking cookies for math class. The recipe calls for 4 4/5 cups of flour. Ashley has to make 1 1/3 times the recipe to feed the whole class. How much flour does Ashley need?

3. Jordan finished her homework in 1 1/2 hours. It took Kasey 3/4 an hour longer than Jordan to finish her homework. How long did it take Kasey?

4. 32.5 divided by -0.08

5. 4.3x= 81.7 (Decimal Equation)

Thank you for helping me if you did!!!!!!!! I really appreciate it very much!!!!!!!

Answers

1) average weight=the sum of weights divided by number of buckets
average weight=(2.79+2.45+2.62)÷3
=2.62

2) recipe calls for 4 4/5=4+(4÷5)
=4.8
1 1/3=1+(1÷3)=4/3
So 4.8 times 4/3=6.4

3) Jordan took 1+1/2=1.5 hours
Kasey 3/4 an hour longer than Jordan
So Kasey took 1.5+(3÷4)=2.25 hours

4) 32.5÷(−0.08)=−406.25

5) 4.3x= 81.7
Solve for x by dividing both sides by 4.3 to get
X=81.7÷4.3
X=19

Hope it helps!

Hello!

1) 2.62

2) 4.8

3) 6.4

3) 2.25 hours

4) −406.25

5) X=19

I hope it helps!

What is 8.478 in expanded form

Answers

Expanded form is the way of writing numbers to see the mathematical value of the individual digits. So the expanded form of 8.478 is 
8+0.4+0.07+0.008

The expanded form of the given number is [tex]8+0.4+0.07+0.008[/tex].

Given:

The given number is [tex]8.478[/tex].

To find:

The expanded form of the given number.

Explanation:

Write the given number as the sum of the place values of its all digits to find the expanded form of the given number.

[tex]8.478=8+0.4+0.07+0.008[/tex]

Therefore, the expanded form of the given number is [tex]8+0.4+0.07+0.008[/tex].

Learn more:

https://brainly.com/question/2208579

Suppose that x is the age of a husband, and y is the age of his wife. if men always marry women who are 3 years younger than themselves, what is the equation for y (wife's age) as a function of x (husband's age)?

Answers

Ok so if the husband is for y and he is 32 and wife is y and she 23 so x-y-32-23 that equals to xy=9

Celia bought a bag of 12 goldfish for $3. What is the cost of 1 goldfish?

Answers

we know that

Celia bought a bag of [tex]12[/tex] goldfish for [tex]\$3[/tex]

so

by proportion

Find the cost of [tex]1[/tex] goldfish

[tex]\frac{3}{12} \frac{\$}{goldfish} =\frac{x}{1} \frac{\$}{goldfish} \\ \\x=3/12 \\ \\x=\$0.25[/tex]

therefore

the answer is

The cost of one goldfish is [tex]\$0.25[/tex]

Celia will pay 0.25 dollars for 1 goldfish. The cost of 1 goldfish is $ 0.25

The Total number of goldfish purchased is 12.

Cost price for 12 goldfish is $ 3.

Let the price of 1 goldfish be x dollars.

Therefore,

[tex]\begin{aligned}x \times\$12&=\$3\\x&=\dfrac{3}{12}\\x&=0.25\end{aligned}[/tex]

Hence, the cost of 1 goldfish is 0.25 dollars.

To know more, please refer to the link:

https://brainly.com/question/1628102?referrer=searchResults

at 7 p.m. last night, the temputure was 10 degrees. At 7 a.m. the next morning, the temputure was -2 degrees. By how much did the temputure change From 7 p.m. to 7 a.m.

Answers

The temperature went down by 12 degrees. (Or you could say it changed by -12 degrees)

10 to 0 =10

0 to -2 = 2

10+2 =12

 it changed by 12 degrees

15/16 is 1 sixteenth groups of what size

Answers

15/16 = 1/16x
(15/16) / (1/16) = x
15/16 * 16/1 = x
15 = x <= 1/16 groups of 15...I think...my mind is trying to comprehend..lol

Differentiate
y=(6x)/(1-cot(x))

Answers

[tex]\bf y=\cfrac{6x}{1-cot(x)}\implies \cfrac{dy}{dx}=\stackrel{quot ient~ru le}{\cfrac{6[1-cot(x)]~-~6x[-csc^2(x)]}{[1-cot(x)]^2}} \\\\\\ \cfrac{dy}{dx}=\cfrac{6-6cot(x)~+~6xcsc^2(x)}{[1-cot(x)]^2}[/tex]

14-9x=-8(10+x) slove and show check

Answers

23x =14 this will be the answer

The next train will arrive in 32 minutes and 30 seconds. In how many seconds will the next train arrive

Answers

you need to multiply the 30 with the 32
60x32=1920 +30= 1950 seconds

An acidophilus culture containing 150 bacteria doubles in population every hour. Predict the number of bacteria after 12 hours.

Answers

150 bacteria doubles every hours.Predict the number of bacteria after 12 hours.

 So 150(2)^12 =  614,400
The answer is 1228800 i hope it helps!

Write y = 2x + 3 using function notation

Answers

f(x) = 2x + 3 i think would be the best way to write it

a jet descended 0.44 mile in 0.8 minute. What was the plane's average change of altitude per minute?

Answers

7.56 because distance decreases

if bx-2=k then x equal

Answers

bx - 2 = k
bx = k + 2
x = (k+2)/b

Hope this helps!

Find a ·
b. |a| = 60, |b| = 30, the angle between a and b is 3π/4.

Answers

Final answer:

To find the dot product of vectors a and b, we can use the formula: a · b = |a| |b| cos θ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.

Explanation:

To find the dot product of vectors a and b, we can use the formula: a · b = |a| |b| cos θ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.

In this case, |a| = 60 and |b| = 30. The angle between a and b is given as 3π/4.

Therefore, a · b = 60 * 30 * cos (3π/4) = 60 * 30 * (-√2/2) = -1800√2.

A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day.

Answers

$819 to make an average 1,000 within 3 day period
(1073 + 1108 + x) / 3 = 1000
(2181 + x) / 3 = 1000
2181 + x = 1000 * 3
2181 + x = 3000
x = 3000 - 2181
x = 819 <=== the restaurant would need to make $ 819

Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of pi/2, and a vertical shift up 3 units.

y =

(I don't have the option to use the characters "/" or "[tex] \pi [/tex]" so they must not be in the answer.

Answers

The period   will change coefficient of x  by  2 pi / pi/2  = 4
and the  vertical shift will  add 3  so its

sin 4x + 3

Hope this helps

Answer:

y = sin 4x + 3

Step-by-step explanation:

A sine function is represented as y = a sin(bx + c) + d

Given values in the question are a = amplitude = 1

period = π/2 = 2π/b

Vertical shift d = 3 units up.

Horizontal shift c = 0

Since 2π/b = π/2

[tex]b=\frac{2\pi }{\frac{\pi }{2}} =\frac{4\pi }{\pi }=4[/tex]

Now the sinusoidal function will be

y = 1. sin( 4x ) + 3

y = sin 4x + 3

Toby is making a picture graph each picture of a book is equal to 2 books he read the row for month 1 has 3 pictures of books how many books did T
oby read during month 1

Answers

5 books because u have to add or multiply

Toby read 6 books during the first month by using the picture graph where each picture represents 2 books.

To determine how many books Toby read during month 1, follow these steps:

Understand each picture of a book represents 2 books read.Observe that Toby has 3 pictures of books for month 1.Multiply the number of pictures by the number of books each picture represents: 3 pictures * 2 books per picture = 6 books.

Toby read 6 books during the first month.

Go has 3 orange pick for every 2 green if ther are 25 picks in all how many picks are orange

Answers

Hello There!

3:2
3 + 2 = 5
25/5 = 5
3 x 5 = 15
2 x 5 = 10
15:10
Therefore 15 orange picks.

Hope This Helps You!
Good Luck :)

Answer:

15

Step-by-step explanation:

It has been given that Go has 3 orange pick for every 2 green.

Hence, the ratio of Go to Green is 3:2

Total number of picks = 25.

Number of picks of orange in 25 picks is given by

[tex]\frac{3}{3+2}\times25[/tex]

Simplifying, we get

[tex]=\frac{3}{5}\times25[/tex]

Multiply the numerator, we get

[tex]=\frac{75}{5}[/tex]

Dividing, we get

[tex]=15[/tex]

Hence, the number of picks of orange are 15.

how do you equally divide 12 cookies with 8 people. what fraction of cookies would each person receive?

Answers

each person would receive 1 and an half cookies.
in other words 1 1/2

Final answer:

To equally divide 12 cookies among 8 people, each person would receive 1 1/2 or 1.5 cookies, which is a fraction of 3/2 per person when simplified.

Explanation:

To divide 12 cookies equally among 8 people, we need to perform a simple division operation where 12 (total number of cookies) is divided by 8 (number of people). Mathematically, this can be represented as 12/8 which simplifies to 1 1/2 or 1.5 cookies per person. This means that each person would receive one and a half cookies.

If the problem requires the answer as a fraction, we can simplify 12/8 by dividing both numerator and denominator by their greatest common divisor, which is 4 in this case. Thus, we get 12/8 = (12÷4) / (8÷4) = 3/2. Therefore, each person gets 3/2 or one and a half cookies.

50779 divided by 590 equals

Answers

50779 / 590 = 86.06610169

But, you can round this to equal 86.1.

What is 51,908 rounded to the nearest hundred dollar?

Answers

The thing we need to do while rounding is look at the digit before. The digit before is 0, meaning we have to round down.So:

51, 900

Hope this helps!
the  9 is the hundred dollar digit  
as the following digit is 0 the answer is  51,900

Can someone please help I need a clear explanation on how to solve this equation.
At Avery Middle School, 273 students responded to a survey asking whether a Bulldog, a Lion, or a Tiger should be the new school mascot. Four times as many students chose Bulldog as chose Tiger. Twice as many students chose Lion as chose Tiger. How many students chose Lion?

Answers

b = amount of students who chose Bulldog

n = amount of students who chose lion

t = amount of students who chose tiger

so.. "t" chose tiger, ok

"Four times as many students chose Bulldog as chose Tiger"
namely, if "t" chose tiger, then 4 times that many chose Bulldog, thus

b = 4t

"Twice as many students chose Lion as chose Tiger"
namely, if "t" students chose tiger, twice as many chose lion

n = 2t

now, we know a total of 273 students were surveyed, thus

[tex]\bf \begin{cases} b+n+t=273\\ \boxed{4t}+\boxed{2t}+t=273 \end{cases} \\\\\\ 7t=273\implies t=\cfrac{273}{7}\impliedby \textit{that many chose \underline{tiger}}[/tex]

Answer:

78 students chose lion.

Step-by-step explanation:

Let x students chose tiger.

Let y students chose bull dog.

Let z students chose lion.

Total students = 273

[tex]x+y+z=273[/tex]           ....(1)

Four times as many students chose Bulldog as chose Tiger.

[tex]y=4x[/tex]

Twice as many students chose Lion as chose Tiger.

[tex]z=2x[/tex]

Substituting the values of y and z in (1)

[tex]x+4x+2x=273[/tex]

=> [tex]7x=273[/tex]

x = 39   (students who chose tiger)

We have to find students who chose Lion or z (defined above)

[tex]z=2x[/tex]

[tex]z=2(39)[/tex]

So, z = 78

Therefore, 78 students chose lion.

Find the standard equation of the circle having the given center (6,-2) and radius 1/5.

Answers

The equation of a circle is (x-h)²+(y-k)²=r², with h being the x value in the center, k being the y value, and r being the radius. Plugging them in, we get 
(x-6)²+(y-(-2))²=(1/5)²
                       =  1/25
                       = (x-6)²+(y+2)²

What is 160,656 rounded to the nearest ten thousandth?

Answers

It would be 160,000.

The nearest two ten thousands would be 160,000 and 170,000

160,656 is 656 away from 160,000, and 9,344 away from 170,000.

It is much closer to 160,000 than 170,000.
160,000 that's rounded to the nearest ten thousandth

Avery's class sold candy bars for a fundraiser. There were 20 bars in each box. Avery sold 4 boxes and an additional 8 bars. Express the total number of boxes that Avery sold as a mixed number. How many candy bars did Avery sell?

Answers

he sold 8 and 4/20 boxes
he solde 8 and 1/5 boxes


he sold 8(20)+4 or 160+4 or 164 candy bars

Answer:

she sold 4 2/5 boxes of candy bars.

In total, she sold 88 bars.

:))

Step-by-step explanation:

For each function f(n) and time t in the table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds

Answers

The question involves estimating the largest problem size a one-teraflop computer can solve in a given time, by equating the time complexity function of the problem to the number of operations the computer can perform per second, and solving for n.

The task is to estimate the largest problem size n that can be solved by a one-teraflop machine within a given time t. A teraflop machine is capable of performing 1012 operations per second. To determine n, we must consider the time complexity function f(n) that describes how the number of operations grows with the size of the problem. Given that the machine can perform 1012 instructions per second, and t is measured in microseconds, we first convert t to seconds.

For example, if the function f(n) follows a linear time complexity, such as f(n) = n, and the computation time t is 1 second, the largest problem size that can be solved is 1012, since the machine can perform 1012 operations in one second.

If the computational complexity is higher, say quadratic as f(n) = n2, we would solve for n in the equation n2 = 1012 to find the largest n that can be solved within 1 second.

Similarly, for more complex functions, we would find the value of n that satisfies the equation f(n) = 1012 * t in seconds, ensuring the result is within the operational constraints of the machine.

Other Questions
Select the correct statement to describe when a sample of liquid water vaporizes into water vapor. Question 12 options: Temperature increases and molecular motion increases while shape becomes less defined. Temperature decreases and molecular motion increases while shape becomes less defined. Temperature decreases and molecular motion decreases while shape becomes more defined. Temperature increases and molecular motion decreases while shape becomes more defined. Find the approximate side length of a square game board with an area of 192 in2. The type of bonding and the numbers of covalent bonds an atom can form with other atoms are determined by __________. which statement explaining why toronto is a major port is fasle List three considerations when you choose memory. what is the value of b if 9+b=-8 What strategies did slaves employ to resist, revolt, and sustain their own independent communities and cultures? how did slaves use white southerners own philosophiespaternalism and christianity, for exampleto their advantage in these efforts? If country a has 163,950 million more computers than country b and the total number of computers for both countries is 314,250 million, find the number of computers for each country List a few of the fundamental principles held by western civilization as a whole What types of scientific claims should be verified Why is theory of evolution a theory what is the molarity of sucrose if 150.0 g is dissolved in 250.0 mL of solution In the mid 19th century harriet beecher stowe was a leader in the struggle for Which is not a power of the president?a. commander in chief of the army/navy/militiab. pardon power in impeachmentc. appoint ambassadorsd. nominate supreme court justicese. make treaties (with advice and consent of senate)? Which has the greater density?air at sea level air at 20 km altitude When sam goes to a restaurant, he always tips the server $2 plus 10% of the cost of the meal. if sams distribution of meal costs has a mean of $9 and a standard deviation of $3, what are the mean and standard deviation of the distribution of his tips? Plzzzz Help mee with the one that isnt answered look at the pic i took A box contains 5 blue marbles 3 red marbles and 6 white marbles. if three marbles are drawn, without replacement, what is the probability that all three are blue? What are the steps to find x 1. What is the algebraic expression for the following word phrase: The quotient of 7 and the sum of 3 and z?A. 3-z ------ 7B. 7 --------- 3-zC. 3+z ----------- 7D. 7 ------------ 3+z2. Write an algebraic expression for the following word phrase: The quotient of 3 and zA. 3 ------ zB. 3 ------- 3zC. 3zD. 3-z3. Which property is illustrated by the following statement: (3z)xy=3(zx)7A. Associative Property Of MultiplcationB. Commutative Property Of MultiplicationC. Inverse Property Of MultiplicationD. Commutative Property Of Addition4. You made two deposits to your bank account this month. One deposit was $17.92, and the second deposit was $15.33. Your balance at the end of the month is $72.31, and you made no withdrawals. Write and evaluate an expression for your balance at the beginning of the month.A. $72.31 + ($17.92 - $15.33)B. $72.31 - ($17.92 - $15.33)C. $72.31 + $17.92 + $15.33D $72.31 - $17.92 - $15.33 Steam Workshop Downloader