F(x)=x^3*125 Complex Zeros (2024)

Mathematics College


Answer 1

Answer: 0

Step-by-step explanation:

[tex]125x^3 =0\\\\x^3 =0\\\\x=0[/tex]

Related Questions

Find the z-scores for the two normally distributed random variables, measured using different units of length.

a) x = 22 in, where X comes from N (15, 2.5)
b) y = 55.88 cm, where Y comes from N (38.1, 6.35)


Using the normal distribution, the z-scores are given as follows:

a) Z = 2.8.

b) Z = 2.8.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

Item a:

The parameters are:

[tex]\mu = 15, \sigma = 2.5[/tex]

Hence the z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22 - 15}{2.5}[/tex]

Z = 2.8.

Item b:

The parameters are:

[tex]\mu = 38.1, \sigma = 6.35[/tex]

Hence the z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55.88 - 38.1}{6.35}[/tex]

Z = 2.8.

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Which point lies on the circle represented by the equation x² + (y-12)² = 25²?
A. (20.-3)
B. (-7,24)
c. (0.13)
D. (-25,-13) ​


Answer: B

Step-by-step explanation: Trust me bro

3. Your new job requires you to calculate the material
costs for manufactured goods. One of goods you
manufacture is a fabric sample in the shape of a circle.
Given the formula A = πr^2, find the
area (A) of the fabric sample whose radius (r) is
7.6 x 10^7 m. Round your answer to the nearest thousandth. (Use 3.14 for π)

A= _____________ m^2


The area of the circular manufactured good is given by:

[tex]A = 1.8146 \times 10^{16} \text{m}^2[/tex]

What is the area of a circle?

The area of a circle of radius r is:

[tex]A = \pi r^2[/tex].

In this problem, the radius in meters is:

[tex]r = 7.6 \times 10^7[/tex]

Hence the area in m² is:

[tex]A = \pi (7.6 \times 10^7)^2 = 181.46 \times 10^{14} = 1.8146 \times 10^{16} \text{m}^2[/tex]

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that any pair of congruent triangles is similar True or false.



yes it's true no problem sir

false! not all congruent triangles will be similar

if x was 4, what is the value of 4x + 3




Step-by-step explanation:





Step-by-step explanation:





hope it helps

3x/2y=11 x+y/2=7 igualacion
Alguien me puede ayudar


La solución del sistema de ecuaciones es igual a (x, y) = (308/47, 42/47).

¿Cómo resolver un sistema de ecuaciones linear por igualación?

Los sistemas de ecuaciones basadas en entidades algebraicas se resuelven mediante procedimientos algebraicos. Grosso modo, el método de resolución por igualación consiste en despejar una variable en dos ecuaciones del sistema para eliminarla y reducir el número de ecuaciones lineales y el número de variables.

A continuación, presentamos una aplicación del método de eliminación:

[tex]\frac{3\cdot x}{2\cdot y} = 11[/tex]

[tex]x = \frac{22\cdot y}{3}[/tex]

[tex]x + \frac{y}{2} = 7[/tex]

[tex]x = 7 - \frac{y}{2}[/tex]

[tex]\frac{22\cdot y}{3} = 7 - \frac{y}{2}[/tex]

[tex]\frac{47\cdot y}{6} = 7[/tex]

y = 42/47

[tex]x = 7 - \frac{y}{2}[/tex]

x = 308/47

La solución del sistema de ecuaciones es igual a (x, y) = (308/47, 42/47).

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B.) (1, -5)

Given, equation:

[tex]\sf \dfrac{(x-1)^2}{25} -\dfrac{(y+5)^2}{49} =1[/tex]

Comparing it with standard formula of hyperbola:

[tex]\sf \dfrac{(x-h)^2}{a^2} -\dfrac{(y-k)^2}{b^2} =1[/tex]

where (h, k) is center

The given equation in standard form:

[tex]\sf \dfrac{(x-1)^2}{5^2} -\dfrac{(y-(-5))^2}{7^2} =1[/tex]


(h, k) = (1, -5)

a = 5, b = 7

So, here (1, -5) is the center of the given hyperbola.

Factor the greatest common binomial factor from each polynomial



=(30x^3-6x^2) + (5x-1)


What is the probability of flipping a coin once and getting heads if you have gotten 5 tails in a row before that?
a. 1/32
b. 1/5
c. 1/4
d. 1/2​



Answer is..... D

Step-by-step explanation:

every single flipping may two results, head or tail.So last one has equal chance.

Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her selections down to six mysteries and nine nonfiction books. If she randomly chooses three books from her selections, what’s the probability that they will all be nonfiction? Enter a fraction or round your answer to 4 decimal places, if necessary.
Please explain in detail


The probability that all 3 books would be nonfiction is 0.1846.

What is the probability?

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that all 3 books would be nonfiction = (number of non fiction books / total number of books) x (number of non fiction books - 1 / total number of books - 1) x (number of non fiction books - 2 / total number of books - 2)

9 /15 x 8/14 x 7/13 = 0.1846

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HELP !! anyone please i need this done in less than in hour JUST ANSWERS WILL DO



Step-by-step explanation:

The scatterplot to the left shows the cost, CCC, in thousands of dollars, and living space, xxx, in square feet (\text{ft}^2)(ft
)left parenthesis, start text, f, t, end text, squared, right parenthesis for several houses in a certain neighborhood. According to the data, which of the following best approximates the cost for an additional square foot of living space for homes in this neighborhood?
Choose 1 answer:
\$80$80dollar sign, 80
\$300$300dollar sign, 300
\$1{,}000$1,000dollar sign, 1, comma, 000
\$13{,}000$13,000dollar sign, 13, comma, 000


According to the data, the cost of this house would increase by 0.08 thousand dollars ($80) for each additional square foot of living space.

How to determine the cost for an additional square foot?

By critically observing the scatter plot, we can logically deduce that it shows a linear trend. Thus, the slope of the line of best fit is given by a ratio of change in cost to the change in living space.

Next, we would approximate two points on the line of best fit and then find the slope as follows:

Slope, m = ΔC/Δx

Slope, m = (C₂ - C₁)/(x₂ - x₁)

Slope, m = (400 - 200)/(4000 - 1500)

Slope, m = 0.08.

Therefore, the cost of this house would increase by approximately 0.08 thousand dollars ($80) for each additional square foot of living space.

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Follow the instructions below to show two different ways of filling a square that has sided of length a + b with triangles and squared without gaps or overlaps.


The proofing for the triangle is illustrated below.

How to illustrate the information?

The proofing for a² + b² = c² in the triangle is illustrated.

It should be noted that the longest side in the triangle is the hypothenuse. The hypothenuse is gotten by finding the square root of the opposite and the adjacent.

Therefore, a² + b² = c²

Let's say a = 3 and b = 4, the value of c will be:

c² = a² + b²

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = ✓25

c = 5

Also, the square and triangle is illustrated and attached.

Learn more about triangles on:



If f(x) =2ײ+2 and g(x) =x² -1, find (f-g) (x)



[tex]\boxed {(f-g)(x) = x^{2}+3}[/tex]

Step-by-step explanation:

Given :

f(x) = 2x² + 2g(x) = x² - 1

Now, this problem can be used using a simple formula.

[tex]\fbox {(f - g)(x) = f(x) - g(x)}[/tex]

Let's solve.

(f - g)(x) = 2x² + 2 - (x² - 1)(f - g)(x) = 2x² - x² + 2 + 1(f - g)(x) = x² + 3

∴ The answer will be x² + 3.

will give brainliest!!



[tex]\huge\boxed{\sf n = 49}[/tex]

Step-by-step explanation:

Given expression:

[tex]x^2-14x+n[/tex] ---------------(1)

We need to solve it using the following formula:


Writing the middle term in the expression as 2ab


Form the expression, we come to now that

b = 7

So, the we can write the expression as:


Comparing expression (1) with the above expression, we get:

n = 49


I need help on this question please help me


The expression that shows the best use of the associative and commutative properties is [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]. The correct option is C. [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]

Associative and Commutative properties

From the question, we are to determine the expression that shows the best use of the associative and commutative properties

The given expression is

[tex]\frac{3}{4}-5+9 -\frac{2}{4}+2[/tex]

To easier simplify the expression, we can group the fractions together and group the whole numbers together

That is,

[tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]

Hence, the expression that shows the best use of the associative and commutative properties is [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]. The correct option is C. [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]

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Please Help Brainliest


Using the z-distribution, the p-value would be of:

b) 0.0086.

What are the hypothesis tested?

At the null hypothesis we test if the means are equal, equivalent to a subtraction of 0, hence:

[tex]H_0: \mu_D - \mu_C = 0[/tex]

At the alternative hypothesis, we test if they are different, hence:

[tex]H_1: \mu_D - \mu_C \neq 0[/tex]

What are the mean and the standard error for the distribution of differences?

For each sample, they are given as follows:

[tex]\mu_D = 12, s_D = \frac{5.2}{\sqrt{73}} = 0.6086[/tex].[tex]\mu_C = 14, s_C = \frac{4.1}{\sqrt{81}} = 0.4556[/tex].

For the distribution of differences, it is given by:

[tex]\overline{x} = \mu_D - \mu_C = 12 - 14 = -2[/tex].[tex]s = \sqrt{s_D^2 + s_C^2} = \sqrt{0.6086^2 + 0.4556^2} = 0.76[/tex]

What is the test statistic?

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.


[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

z = -2/0.76

z = -2.63.

Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.

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What is the measure of arc RT


The measure of arc RT is 156 degree.

Measure of arc RT


arc TRM=102°


arc RST=2×1O2°

arc RST=204°

Measure of arc RT

arc RT= 2(180° - 102°)

arc RT = 2(78°)

arc RT = 156 degrees

Therefore the correct option is B.

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Marco has joined a bowling league, and is trying to raise his average to 130. On his last four games he scored 128, 127, 123, and 122. How much will he need to score on the next game to raise his mean to 130?


The score Macro needs in his next game to have a mean of 130 is 150.

What should be the next score?

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

130 = (128 + 127 + 123 + 122 + x) / 5

Where x represents the fifth score

130 = (500 + x) / 5

130 x 5 = 500 + x

650 = 500 + x

650 - 500 = x

x = 150

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The graph of a quartic function crosses the x-axis at -4 and -2 and touches it at 3. State the equation for the family.


The equation of the quartic function is f(x) = x⁴ - 18 · x² + 6 · x + 72.

How to find the possible equations for a quartic polynomial that passes through the x-axis at three points

Herein we must construct at least a polynomial that satisfies all conditions described in the statement. According to the fundamental theorem of algebra, quartic functions may have no real roots, two real roots or four real roots, which means that one of the roots must have a multiplicity of 2.

The root with a multiplicity of 2 is x = 3 and both x = - 4 and x = - 2 have only a multiplicity of 1, then we have the following expression by using the factor form of the definition of polynomials:

f(x) = (x - 3)² · (x + 4) · (x + 2)

Now we expand the expression to get the standard form:

f(x) = (x² - 6 · x + 9) · (x² + 6 · x + 8)

f(x) = x⁴ - 6 · x³ + 9 · x² + 6 · x³ - 36 · x² + 54 · x + 8 · x² - 48 · x + 72

f(x) = x⁴ - 18 · x² + 6 · x + 72

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Christine is putting money into a savings account. She starts with $650 in the savings account, and each week she adds $60. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Christine has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 11 weeks.


Total amount of money in the savings account after 11 weeks is $1310.

Total money in the account =

Initial Money + Money added per week x Number of weeks


Initial Money = $650

Money added per week = $60

Total money in the account = S

Number of weeks = W

Substituting it in the above equation we get,

S = $650 + $60xW (General Equation)

Total amount of money in the savings account after 11 weeks

S = $650 + $60x11

S = $650 + $660

S = $1310

Thus total amount of money in the savings account after 11 weeks is $1310.

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You are buying a house and you are financing the purchase with a mortgage of $130,000. The mortgage has a 30 year term and requires monthly payments. The mortgage charges an interest rate of 0.3% every month. What is the total interest payment over the life of the mortgage?



130,000 -:- by 30 x 0.3 x 12 = 15,600.

Step-by-step explanation:

(I hope its right, Im not good at math)

C(x) = 12000 + 400x − 2.6x2 + 0.004x3
is the cost function and
p(x) = 1600 − 8x
is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)


Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

How to find the production level that'll maximize profit?

The cost function, C(x) is given by 12000 + 400x − 2.6x² + 0.004x³ while the demand function, P(x) is given by 1600 − 8x.

Next, we would differentiate the cost function, C(x) to derive the marginal cost:

C(x) = 12000 + 400x − 2.6x² + 0.004x³

C'(x) = 400 − 5.2x + 0.012x².

Also, revenue, R(x) = x × P(x)

Revenue, R(x) = x(1600 − 8x)

Revenue, R(x) = 1600x − 8x²

Next, we would differentiate the revenue function to derive the marginal revenue:

R'(x) = 1600 - 8x

At maximum profit, the marginal revenue is equal to the marginal cost:

1600 - 8x = 400 − 5.2x + 0.012x

1600 - 8x - 400 + 5.2x - 0.012x² = 0

1200 - 2.8x - 0.012x² = 0

0.012x² + 2.8x - 1200 = 0

Solving by using the quadratic equation, we have:

x = 220.40 or x = -453.73.

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

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Savings account at a bank pays 5% simple interest in account at Bank B pays 2% compounded interest the table shows the balance in each account after an initial deposit of $1000 which describes the balance after a long period of time



The balance in Bank B will be greater.

Step-by-step explanation:

Because simple interest is just interest on the principle only which is 50 every year doesn't change but with compound interest you will get 2% Interest every year. principle+interest

Charlotte owns two entertainment websites. Here are some details about those
websites for one entire month:
Number of writers
Number of posts posted
Average number of words of post
Average likes per post
Average comments per post
Number of new subscribers
Profit (Revenue-Expenses)
Website A Website B
Charlotte wants to know which website produces a larger amount of content per a
single writer.
1) Charlotte thought of two different ways to define this quantity, Identify these two
definitions among the following options.
4 of 4


In order to define the quantity of which of the two website produces a larger amount of content per single writer, Charlotte thought of:

A Average number of posts per writer C Average number of words per writer

How can Charlotte define the quantity?

Charlotte wants to know which website has more content per writer which means that she wants to know which website is more productive with writing.

One way she can do this is to check the average number of posts per writer per website. This would show her which website has a writer that writes more content on average.

Charlotte could also use average number of words per writer. This shows just how much writing the writers in each websites are doing, in terms of words. The website with the higher average words per writer is therefore providing more content.

Options for this question include:

A Average number of posts per writerB Total number of wordsC Average number of words per writerD Average number of likes per word

Find out more on using averages as decision tools at https://brainly.com/question/17004212.


Geometry Question!! PLEASE HELp


The difference between the distance travelled by any point on the record and it's label is; 27.57cm.

What is the difference between the distance travelled in each case?

According to the task content, it follows from observation that the quantity required is the difference between the circumference in each case and can be evaluated as follows;

Difference = π(17.78 - 9)

Difference = (22/7) × 8.78

Difference = 27.57cm.

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help me pls: what is
four and two eighths minus two and five eighths equals




Step-by-step explanation:

4 2/8 - 2 5/8

34/8 - 21/8 = 13/8

1 5/8 as a mixed fraction

Draw the graph of changing length of shadow of a stick from 12pm to 5pm.


The graph of changing length of shadow of a stick from 12pm to 5pm shows that length of shadow increases.

When an object (like the stick in the cartoon) blocks some of the Sun's light, it casts a shadow. The shadow always points away from the Sun. How long the shadow is depends on how low or high the Sun is in the sky. If the Sun is low, we see a longer shadow. Is the Sun is high, we see a shorter shadow.

Length of shadow due to the Sun's light is smallest when the Sun is vertically above. This happens at 12 noon.

Thus the graph of changing length of shadow of a stick from 12pm to 5pm shows that length of shadow increases.

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An 8ft length of 4 inch wide crown molding cost $13. How much it cost to buy 88ft of crow molding


The amount it costs to buy 88ft of crow molding is; $143.

How much does it cost to buy 88ft if crow molding?

It follows from the task content that the cost for 8ft length of a specific width crown molding is; $13.

On this note, it follows that the cost of buying 88ft of the same kind of crow molding can be estimated as;

88 × ($13/8)

= $143.

Therefore, the cost of 88ft of crow molding is; $143.

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A rock is dropped from a height of 100 feet. Calculate the time between when the rock was dropped and when it landed. If we choose "down" as positive and ignore air friction, the function is h (t) = 36t2 - 64
t= 3.56 seconds
t= 1.78 seconds
t= 1.33 seconds
t= 8 seconds


The time it takes between when the rock was dropped and when it landed is 1.33 seconds.

What is the time it takes for the rock to land?

The time it takes the rock to land on the ground from where it is dropped can be determined by using the function given.

The height of the function when it hits the ground will be zero, so the function can be written as:

[tex]\mathbf{h(t) =36t^2 -64}[/tex]

[tex]\mathbf{0 =36t^2 -64}[/tex]

64 = 36t²

[tex]\mathbf{t^2 = \dfrac{64}{36}}[/tex]

t² =1.778

[tex]t = \sqrt{1.778}[/tex]

t = 1.333 seconds

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F(x)=x^3*125 Complex Zeros (2024)


How do you find the complex zeros of an equation? ›

Algebraically, these can be found by setting the polynomial equal to zero and solving for x (typically by factoring). Graphically, this can be seen where the polynomial crosses the x-axis since the output of the polynomial will be zero at those values.

What is the zero of x3 125? ›

The solution to the equation x3 - 125 = 0 is x = 5. Our equation is a cubic equation that contains just one variable term.

How do you factor F with complex zeros? ›

To use complex zeros to factor a polynomial function f(x), follow these steps:
  1. Find the complex zeros of the polynomial function. ...
  2. Write down the complex zeros in pairs of conjugates. ...
  3. For each pair of complex conjugate zeros, create a quadratic factor of the form.
  4. Expand the quadratic factors and simplify.

What is the value of x in x3 125? ›

Answer and Explanation:

The value of is x is 5. To solve this, put cube root on both sides: ∛x^3 = ∛125. Evaluate the problem. We know that 5 * 5 * 5 = 125.

What are the zeros of a complex function? ›

Zeros of a Complex Function

z = a in D if and only if the f(n)(a) = 0 for n = 1, 2, 3, …., k – 1 but f(k)(a) ≠ 0. A zero of order one is known as a simple zero. Hence, f has a zero at z = 0 of order 3.

How do you solve for zeros in an equation? ›

As we learned, finding the zero of a function means to find the point (a, 0) where the graph of the function and the y-intercept intersect. To find the value of a from the point (a, 0), you need to set the function equal to zero and then solve for x.

What is the real solution of the equation x3 125? ›

x3=125 Three solutions were found : x =(-5-√-75)/2=(-5-5i√ 3 )/2= -2.5000-4.3301i x =(-5+√-75)/2=(-5+5i√ 3 )/2= -2.5000+4.3301i x = 5 Rearrange: Rearrange the equation by subtracting what is ...

How many zeros does 125 have? ›

power of a prime p in n! Hence no of zeros in 125! =25+5+1=31. Hence there are 31 zeros in 125! .

What are trailing zeros of 125? ›

Hence, the answer is 31. Zeroes at the end of 125!

How do you find the zeros of a function F? ›

To find the zeros of a function f(x), we solve the equation f(x) = 0 for x. To find the roots of a function, we can use different methods to factorize. We can factorize the function using various methods such as: Grouping.

How do you factor to find zeros? ›

Step 1: Set your first factor equal to zero and solve. Step 2: Continue to set your factors equal to zero and solving until you have done this to all of the factors in your factored form polynomial. This factor does not give any real solutions. Step 3: List all of the zeros of your polynomial.

How many complex zeros does a function have? ›

Every polynomial function of positive degree n has exactly n complex zeros (counting multiplicities). For example, P(x) = x [ 5 ] + x [ 3 ] - 1 is a 5 [ th ] degree polynomial function, so P(x) has exactly 5 complex zeros.

Is x3 equal to 125? ›

The value of the cube root of 125 is 5. It is the real solution of the equation x3 = 125.

What x 3 is 125? ›

In fact, 125 = 5^3. So the only two whole numbers (greater than one) that multiply to produce 125 are 5 and 5^2, i.e. 5 and 25.

How do you find the number of complex roots in an equation? ›

No of complex roots = No of total roots - No of real roots .

What is the formula for finding a complex number? ›

The complex number is basically the combination of a real number and an imaginary number. The complex number is in the form of a+ib, where a = real number and ib = imaginary number. Also, a,b belongs to real numbers and i = √-1.

How do you find the order of zeros in complex analysis? ›

A zero is of order n if 0 = f (z0) = f (z0) = ··· = f(n−1)(z0), but f(n)(z0) = 0. A zero of order one (i.e., one where f (z0) = 0) is called a simple zero. Examples: (i) f(z) = z has a simple zero at z = 0.

How do you solve complex numbers over equations? ›

To solve an equation that has a complex number as a solution: Work with the purely real valued terms until no further simplification can be done and all that remains is an answer involving a negative radicand. Rewrite the complex root as the square root of a real number times the square root of -1.

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