For The Polynomial Function (x) = X4 16x2, Find The Zeros. Then Determine The Multiplicity At Each Zero (2023)

Mathematics High School


Answer 1

Our function f(x) can be rewritten if we factor out a common x^2 from each term:

Now inside the parentheses we have a polynomial of the form a^2 - b^2, or the difference of two perfect squares, which can be factored as (a+b)(a-b) so we have:

Setting our function equal to zero gives us the roots x = 0, x = 4, and x = -4.
The multiplicity of the root zero is two since it occurs twice, and the others are one since they occur only once. If you graph the function you can see that it will only touch the x-axis at x = 0, but will cross the x-axis at x = 4 and x = -4.

Related Questions

Luann has a piece of ribbon that is 1 yard long. She cuts 33 inches off to tie a gift box. How many inches of ribbon are not used?


First, we convert the given initial length of the ribbon by the conversion factors,
1 yd = 3 ft
1 ft = 12 inches
(1 yd)(3 ft/ 1 yd)(12 in/1 ft) = 36 in
Since Luann used 33 inches, the length of the unused ribbon is 3 inches.

The line y=5x+b is tangent to the graph y=/x at the point P= (a,/a) Find P and determine b. / means square root


P = (1/100 , 1/10)
b = 1/20
Equate both equations. Use the substitution y=/x (/ means square root). Obtain an equation in terms of y. 5y2 - y +b = 0 Use b2 - 4ac = 0 for tangent. You'll get the answer for b then replace in equation, overall 5y2 - y + 1/20 = 0. Use the quadratic formula to solve for y. You'll obtain y = 1/10 as answer. Using the substitution y=/x, x=y2, x = (1/10)2 = 1/100, /x = 1/10. 5y2 and (1/10)2 are the square....5y to the power of 2.

Rewrite x - 2y = 8 using function notation.


x - 2y = 8 then it is y = 0.5x-4.

Hope I helped! ( Smiles )

andy said that 4/9 of his collection is *action* or * comedy* cynthia said that andy made an error explain whether andy is correct and why


Andy is correct when he saidthat 4/9 of his collection is *action* or * comedy*. On the other hand, Cynthia is wrong when she said that Andy made an error explain about his collection. Based on the given problem, it is accurate to say that Andy is correct about his collection.

How many square inches are in 8 square feet? brainliest if u are right.


Theres 12 inches in a foot. So 12x8=96

Find the interquartile range of 17, 23, 8, 5, 9, 16, 22, 11, 13, 15, 17, 18


The answer is 13 because 22-9 equals 13.

(Video) How to Determine the Multiplicity and Zeros of a Polynomial


Hope I helped! ( Smiles )



Simplifying 4x2 + -24x + 4y2 + 72y = 76
Reorder the terms: -24x + 4x2 + 72y + 4y2 = 76
Solving -24x + 4x2 + 72y + 4y2 = 76
Solving for variable 'x'.
Reorder the terms: -76 + -24x + 4x2 + 72y + 4y2 = 76 + -76
Combine like terms: 76 + -76 = 0 -76 + -24x + 4x2 + 72y + 4y2 = 0
Factor out the Greatest Common Factor (GCF), '4'. 4(-19 + -6x + x2 + 18y + y2) = 0
Ignore the factor 4.

Subproblem 1
Set the factor '(-19 + -6x + x2 + 18y + y2)' equal to zero and attempt to solve: Simplifying -19 + -6x + x2 + 18y + y2 = 0 Solving -19 + -6x + x2 + 18y + y2 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.
The solution to this equation could not be determined.

The mean test scores with standard deviations of four English classes are given below. Class
Standard Deviation
Mrs. Jones
Mrs. Rijo
Mr. Phan
Mrs. Scott

Which statement is most likely to be true?
The scores of Mrs. Scott’s class are the closest to the class mean.
The scores of Mr. Phan’s class are the closest to the class mean.
The scores of Mrs. Jones’s class are the closest to the class mean.
The scores of Mrs. Rijo’s class are the closest to the class mean.


The closeness of the scores to the mean value is reflected through the values of the standard deviation. The smaller the value of standard deviation, the closer are the individual values to the mean. Therefore, since Mrs. Rijo's class has the smallest value for the standard deviation, her class has the closest individual score to the mean. The answer is the fourth choice.


Your answer is b!

Step-by-step explanation:

In a circle, a 90°sector area 36 what is the radius of the circle


solve for "r"

7 less than three times m is n


Your answer is 3m-7=n

If it's 4 less than 2 times a number if would be
2x - 4

During one month there were 7 days of precipitation.What if there had only been 3 days of precipitation that month?How would that change the measures of center?


We've hit on a case where ameasureofcenter doesnot provide all the information spread or variabilitythereisin month-to-month precipitation. based on how busy eachmonth has been inthe past, lets managers plan Unit 6: Standard Deviation | Student Guide | Page3Ifyou sum the deviations from the mean, (. ).

True or False cos^2x=(1-cos2x)/2

(Video) How to Find Zeros, Multiplicity and End Behavior to Graph of a Polynomial




Step-by-step explanation:

From the trigonometric identity: cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y) we can get:

cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y)

cos(x+x) = cos(x)*cos(x) - sin(x)*sin(x)

cos(2x) = cos^2(x) - sin^2(x)

cos^2(x) = cos(2x) + sin^2(x) (eq. 1)

From the trigonometric identity: cos^2(x) + sin^2(x) =1 we can get:

cos^2(x) + sin^2(x) = 1

sin^2(x) = 1 - cos^2(x) (eq. 2)

Replacing equation (1) into equation (2) we get:

cos^2(x) = cos(2x) + 1 - cos^2(x)

cos^2(x) + cos^2(x) = 1 + cos(2x)

2*cos^2(x) = 1 + cos(2x)

cos^2(x) = [1+cos(2x)]/2


(My answer on Apex was correct)

given the points A(-3,-4) and B(2,0), point P (-1,-12/5) partitions AB in the ratio A. 1:3 B. 2:1 C. 2:3 D. 3:2


The point P (-1,-12/5) partitions the given line AB into two line segments with ratio: C. 2:3

How to divide lines into segments?

We are given the coordinates;

A(-3,-4) and B(2,0)

Now, P(-1,-12/5) partitions line AB

The point (-1, -12/5) lies on the line from A to B, but not in the center.

Thus, by using length of a line segment formula, we have;

AP = √[(-1 - (-3))² + (-12/5 - (-4))²] =

AP = √[2² + 1.6²] =

AP = √6.56

AP = 2.561

PB = √[(-1 - 2)² + (-12/5 - 0)²]

PB = √[(-3)² + (-12/5)²]

PB = √14.76

PB = 3.842


AP:PB = 2.561 : 3.842 This is approximately a ratio of 2:3

(Video) Find a Polynomial Function Given the Zeros, Multiplicity, and (0,a) (Degree 3)

Thus, the point P partitions AB into two line segments with ratio 2:3

Read more about division of line segements at;

Forotherratiosbesides the 1 to 1ratio, it is necessary to determine the total Point Pdivides segmentABinto a2/3 ratio, there are two sections between A and P GiventhepointsA(-1,2) andB(7, 8), determine the coordinates ofpoint Pon Solution: Method 1: A1/3 ratiodivides the segment into 1 +3=4equal parts.

Evie was doing a science fair project by surveying her biology class. she found that out of 30 students, 15 had brown hair and 17 had blue eyes and 6 had neither. determine the number of students that had brown hair and blue eyes.


Since there are 6 students with neither brown hair nor blue eyes, the remaining number of students with at least one of the characteristic is 24. The sum of the students with brown hair only, with blue eyes only, and with both should be equal to 24. By letting x be the number of students with both, the equation that would best represent the given is,
(15 - x) + x + (17 - x) = 24
The value of x from the equation is 8.

What is the sum of 15*8


Fifteen times eight is 120.

I hoped this helped! Please rate, thank, and pick the Brainliest answer (not necessarily mine!). Thanks, it really helps! :)

15 *8 is 120 my friend

What is the multiplicative rate of change of the function A) 1/3
B) 2/3
C) 2
D) 9

X. Y
1. 6
2. 4
3. 8/3
4. 16/9


Answer: B

Step-by-step explanation:

From the given table

When x changes from 1 to 2 , value of y changes from 6 to 4

The multiplicative rate of change=

Similarly we can check

When x changes from 2 to 3 , value of y changes from 4 to

The multiplicative rate of change=

When x changes from 3 to 4 , value of y changes from to

The multiplicative rate of change=

Therefore, the multiplicative rate of exponential function =



Step-by-step explanation:

We have been given a table of values. We are asked to find the multiplicative rate of change of our given function.


(Video) Find the Zeros of a Polynomial and Their Multiplicities

x y

1 6

2 4

3 8/3

4 16/9

We know that the multiplicative rate of change of a function is the number by which each next term of an exponential function is increasing or decreasing.

We can find multiplicative rate of change by dividing any term of the function by its previous term.

Therefore, the multiplicative rate of change of our given function is and option B is the correct choice.

Danica is arranging flowers for a party. On each table, t, there will be a vase of 9 flowers and 3 bowls of flowers with f flowers inside. Danica needs an additional 12 flowers for a cake topper. This situation can be written as the following expression: 9t + (3f)t + 12

How many flowers should Danica purchase if she has 21 tables with 3 flowers in each bowl?


On this question, we can use the order of operations. ( pemdas )

First, we must fill in the missing numbers.
9*21 + (3*3)21 + 12

Start in the parentheses.
(3*3)21 = 9*21 = 189

The rest is just addition now!

390 is the correct answer.

The correct answer is D. 390

Write y=-5x^2+15 in vertex form


In vertex form it will look like this

y = −5 (x+0) 2 + 15

Cumpute the standard deviation for 13.3,14.3,15.3,16.3, 17.3


The standard deviation is 1 14.3-13.3 = 1 15.3-14.3 = 1

Ugh v.v 6.96 rounded to the nearest tenth??


9 is closer to 10

6 (the second one) is closer to 10

So, the answer youre looking for is 7.0

Good Luck! :)

(Video) Find the zeros and give the multiplicity | f(x) = x^2(2x + 3)^5(x − 4)^2

I believe that it's 7.


How do you find the multiplicity of a zero in a polynomial function? ›

This means that if x = c is a zero, then p ( c ) = 0 . The zeros correspond to the x-intercepts of the polynomial. Multiplicity: The multiplicity of a zero, x = c, is the number of times the factor appears in the fully factored form of the polynomial. This is equal to the exponent on the factor.

How many zeros does the polynomial x 3 2 4 can have? ›

In conclusion, the polynomial (x – 3)² – 4 has two zeros, x = 1 and x = 5, and can be written in factored form as (x – 1)(x – 5).

What are the zeros and multiplicities calculator? ›

A Multiplicity Calculator works by calculating the zeros or the roots of a polynomial equation. A polynomial equation a x 2 + b x + c usually intercepts or touches the x axis of a graph; the equations are solved and are put equal to zero to calculate the roots of the equation.

How do you calculate multiplicity? ›

In this case spin multiplicity = [(+n) + (-n) + 1], where, n = number of unpaired electrons in each alignment.

What is multiplicity of zeros example? ›

A zero has a "multiplicity", which refers to the number of times that its associated factor appears in the polynomial. For instance, the quadratic (x + 3)(x − 2) has the zeroes x = −3 and x = 2, each occuring once.

What is the multiplicity of a polynomial? ›

The multiplicity of a root affects the shape of the graph of a polynomial. Specifically, If a root of a polynomial has odd multiplicity, the graph will cross the x-axis at the the root. If a root of a polynomial has even multiplicity, the graph will touch the x-axis at the root but will not cross the x-axis.

How do you find the zeros of a polynomial from a graph? ›

If we graph this polynomial as y = p(x), then you can see that these are the values of x where y = 0. In other words, they are the x-intercepts of the graph. The zeros of a polynomial can be found by finding where the graph of the polynomial crosses or touches the x-axis.

What is the zeros of a polynomial? ›

Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole. A polynomial having value zero (0) is called zero polynomial. The degree of a polynomial is the highest power of the variable x. A polynomial of degree 1 is known as a linear polynomial.

When a polynomial x4 5x3 4x2 10x 12 has two zeros? ›

Solution: As given polynomial x4+5x3+4x2−10x−12 has two zeroes as −2 and −3.

What are all the zeroes of the polynomial 2x3 4x x2 2 if two of its zeroes are 2 and 2? ›

Hence, all the zeroes of cubic polynomial are 1 2 , 2 , - 2 .

What are all zeros of the polynomial 2x 4? ›

Therefore, the zero of the polynomial 2x - 4 is 2.

How do you find the number of zeros in a polynomial? ›

In order to determine the positive number of real zeroes, we must count the number of sign changes in the coefficients of the terms of the polynomial. The number of real zeroes can then be any positive difference of that number and a positive multiple of two.

How do you find the zeros of a polynomial graph? ›

If we graph this polynomial as y = p(x), then you can see that these are the values of x where y = 0. In other words, they are the x-intercepts of the graph. The zeros of a polynomial can be found by finding where the graph of the polynomial crosses or touches the x-axis.

Can a zero have a multiplicity of 4? ›

Since (−x)4=(−1)4x4=x4 ( − x ) 4 = ( − 1 ) 4 x 4 = x 4 , the zero 0 has multiplicity 4.


1. Find zeros, multiplicity and crosses, touches and or turns
2. Determining the Zeros of Function and It's Multiplicity
(Brian McLogan)
3. Find Zeros of the Polynomial Function f(x)=x^3+4x^2-16x-64 and State The Multiplicity of Each Zero
4. Finding the zeros and multiplicity of polynomials
5. How To Graph Polynomial Functions Using End Behavior, Multiplicity & Zeros
(The Organic Chemistry Tutor)
6. Find the zeros and give the multiplicity | f(x) = 4x^5 − 12x^4 + 9x^3
(The Glaser Tutoring Company)


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