Which of the following describes the roots of the polynomial function f (x) = (x + 2) squared (x minus 4) (x + 1) cubed?
–2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3
–2 with multiplicity 3, 4 with multiplicity 2, and –1 with multiplicity 4
2 with multiplicity 2, –4 with multiplicity 1, and 1 with multiplicity 3
2 with multiplicity 3, –4 with multiplicity 2, and 1 with multiplicity 4

Answers

Answer 1

Answer:

A

Step-by-step explanation:

[tex]f(x) = (x + 2)^2(x-4)(x + 1)^3[/tex]

x+2=0

x+2-2=0-2

x=-2.....(x+2) was squared...exponent of 2...multiplicity of 2

x-4=0

x-4+4=0+4

x=4....(x-4) has no visible exponent which means it is essentially to the power of 1...multiplicity of 1

x+1=0

x+1-1=0-1

x=-1....(x+1) was cubed...exponent was 3...multiplicity of 3

Answer 2

The roots and their respective multiplicity are –2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3 thus option (A) is correct.

What are the roots of an equation?

The roots of an equation are the solution of that equation, since an equation consists of hidden values of the variable so to determine them by different processes and then the resultant is called roots.

For example root of x -4 = 0 is x = 4 so 4 will be the only root of this linear equation.

As per the given function,

f(x) = (x + 2)²(x - 4)(x + 1)³

The roots are the points at which the value of the function is zero.

f(x) = 0

(x + 2)²(x - 4)(x + 1)³ = 0

(x + 2)² = 0

x = -2 (with a multiplicity of 2)

(x - 4) = 0

x = 4  (with a multiplicity of 1)

(x + 1)³ = 0

x = -1  (with a multiplicity of 3)

Hence "The roots and their respective multiplicity are –2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3 thus option (A) is correct".

To learn more about the roots of equations,

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Related Questions

¿ Qué porcentaje de 70 es 35?

Answers

Answer:

Step-by-step explanation:

50% mi amigo

According to Bill Nye, How many people need to be in a room for there to be 50% chance of atleast 2 people having the same birthday?a. 128 b. 56 c. 29 d. 12

Answers

Answer:

the answer is actually 23 people

Step-by-step explanation:

Bill Nye's birthday paradox can be explained in the following manner:

first we must find the probability that in a room with 23 people, no two people have the same birthday

probability of no two people having the same birthday = 365/365 x 364/365 x 363/365 x 362/365 ... you keep multiplying until 343/365 = 0.492703

so the probability that in a room with 23 people, no two people have the same birthday = 49.2703%

the probability of two people having the same birthday = 1 - probability of no two people having the same birthday = 1 - 49.2703% = 50.7297%

x2 + 5x +4=0
How do we do this

Answers

Answer: x=−1 or x=−4

Step-by-step explanation: Solve by factoring

Answer:

(x+1)(x+4)

Step-by-step explanation:

Given that R= 4x +6y find x when y= 4 and R=11

Answers

Answer:

The value of x:

[tex]x=-\frac{13}{4}[/tex]

Step-by-step explanation:

Given the equation

[tex]R=4x+6y[/tex]

substituting the values y=4 and R=11

[tex]R=4x+6y[/tex]

[tex]11=4x+6\left(4\right)[/tex]

[tex]11=4x+24[/tex]

[tex]11-24=4x[/tex]

switching the sides

[tex]4x=11-24[/tex]

Subtract the numbers: 11-24=-13

[tex]4x=-13[/tex]

Divide both sides by 4

[tex]\frac{4x}{4}=\frac{-13}{4}[/tex]

[tex]x=-\frac{13}{4}[/tex]

Therefore, the value of x:

[tex]x=-\frac{13}{4}[/tex]

Gretta wants to buy a jar of fossils that is 10% off. The original price is
$47.82.
What is amount of discount (nearest penny)?

Answers

Answer:

4.78

Step-by-step explanation:

=47.82 x 10/100

=47.82 x 1/10

=4.782

=~ (approx) 4.78

HELP PLEASE HELP ILL GIVE U 15 points and BRAINLIEST to the correct answer (DONT guess please)

Consider the function.
f (x)= -80 +4
What is the value of f (-1/4)?
A. 0
B.2
C. 3
D. 6

Answers

It should be C. 3.
Yes

Answer: the answer is b

Step-by-step explanation:

Just trust me

The number 0.003 is 1/10 of which decimal?

Answers

Answer:

I'd say it's 0.03

Step-by-step explanation:

0.03 divided by 10 is 0.003 so it's 1/10

0.003 is 1/10th of 0.03.

What is a decimal ?

A decimal is represented by a point or a dot it separates the decimal part and the fractional part for example 24.75 here the whole part is is 24 and the fractional part is 75.

if we divide 0.03 by 10  = [tex]\frac{0.03}{10}[/tex] = 0.003.                     (dividing a number by 10

                                                                                    moves the decimal point

                                                                                    to the left by 1 because                      

                                                                                    10 has 1 no. of zeroes)

Learn more about decimals here :

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If ƒ (x ) = 3x2 - x, find ƒ (-2).

Answers

Answer:

f(-2) is 14.

Step-by-step explanation:

We have been given the function:

We have to find f(-2)

That means put x= -2 in the given function we get:

After simplification we will get:

After further simplification we will get the required result:

 Hence, ƒ (-2) is 14

A cold water pipe can fill a swimming pool in 4 hours, and a hot water pipe in 6 hours. If cold water pipe is turned on and hot water pipe is turned on 3 hours later then how long will it take them to fill the pool together?

Answers

answer = 5

Step-by-step explanation:

A cold water pipe can fill a swimming pool in 4 hours

And a hot water pipe in 6 hours.

If cold water pipe is turned on and hot water pipe is turned on 3 hours later

6-4 = 2

2+3 = 5

5 answer

Answer:

0.6 of an hour

Step-by-step explanation:

A cold pipe takes 4h hours so we can assume ¼ of our job is done in one hour.

After 3 hours go by with the cold pipe on, we have ¼ of the job left.

Now we have our hot pipe, which takes 6 hours for the entire pool, so we can assume that it has a rate of ⅙ per hour. Now since these two pipes are working together we can add them.

⅙ + ¼ = ⁵/₁₂

Now we divide.

Since at the start 3 hours had gone by with the cold pipe that would have been ¾ of our time so, 1 - ¾ = ¼

¼ ÷ ⁵/₁₂ = ⅗ or 0.6 of an hour

James says that 12 is a common factor of 3 and 4. June says that 12 is a common multiple of 3 and 4. Who is correct?

Answers

Answer:

June is correct.

Step-by-step explanation:

June is correct because Common Multiples are what we get after multiplying the number while common factors are what we can multiply to get the number.

What fraction is equivalent to the decimal and percent below? Enter your
answer in simplest form, using the slash (/) as the fraction bar.
Fraction Decimal Percent
? 0.50 50%
Answer here
SUBMIT

Answers

Answer: 1/2

Step-by-step explanation:

PLS HELP DONT ANSWER IF YOU DONT KNOW ALSO I WILL MARK BRAINLIEST

Answers

Answer: Absolute value is always positive so the two negative answers can’t be it. The plotted dot is also clearly past 1 on the number line so .75 doesn’t make sense either. The only logical answer is 1.25
i’m pretty sure it’s a

HELP EMERGENCY!!!! (2.5 x 10-10) (7 x 10-5)
Express your answer in scientific notation.

Answers

Answer:

[tex]1.75[/tex] × [tex]10^{-15}[/tex]  

I hope this helps!

0.2 4/15 0.21 1/4 in least to greatest

Answers

Answer:

0.2, 0.21, 0.25 (1/4), 0.2666666 (4/15)

Step-by-step explanation:

Given h (x) = -x -3, find h (-6)

Answers

Answer:

h(-6) = 3

Step-by-step explanation:

h(x) = -x - 3 when h(-6).

~Substitute

h(-6) = -(-6) - 3

~Simplify

h(-6) = 6 - 3

~Subtract

h(-6) = 3

Best of Luck!

mumbai is 845 km away from bangalore whats that distance in cm

Answers

It should be 84500000 centimeters.

PLEASE HELP FAST & CORrect 50 POINTS

Answers

Answer:

105

Step-by-step explanation:

Evaluate this expression when p = 4 and q = -2:
4(√p+q²)

A. 4
B. -8
C. 12
D. 24

Answers

4(root4+(-2)^2)= 4(2+4)=4(6)=24

Answer:

24

Step-by-step explanation:

Please help please help

Answers

Answer:

Do Y divided by X.

Step-by-step explanation:

This is normally what I do so hope I helped.

Can someone please tell me if I got this right or wrong? I’ll give brainliest
Please be honest

Answers

Answer:

yes your answer is correct

Step-by-step explanation:

Jimmy earns money for babysitting his little
brother. He earns the same amount every
week. He is saving all the money he earns for a
summer trip. The table shows how Jimmy's
savings have been growing.

Answers

I need the table and the answer choices to help you though

Compute 41, 42, 43, 44, 45, 46, 47, and 48. Make a conjecture about the units digit of 4n where n is a positive integer. Use strong mathematical induction to prove your conjecture.

Answers

Answer:

The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even

Step-by-step explanation:

[tex]4^1 = 4\\4^2 = 16\\4^3 = 64\\4^4 = 256 \\4^5 = 1024\\4^6 = 4096\\4^7 = 16384\\4^8 = 65536[/tex]

The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even

To prove this conjecture

[tex]4^1 = 4\\4^2 = 16[/tex] unit digit = 6

hence the property is true for ; n = 1 and n = 2 and also for every odd and even number ( i.e. from 1  to 8 )

Sarah graphed the function. y =-1/2x+4 if the domain is restricted to this on the photo what’s the answer I pick

Answers

Answer:

Option (4)

Step-by-step explanation:

Domain of a function is defined by the x-values or input values of the function.

Similarly, Range of a function is defined by the y-values of output values for the corresponding input values.

From the graph attached,

Domain is restricted to 0 ≤ x ≤ 8.

Therefore, Range will be 0 ≤ y ≤ 4.

Option (4) will be the answer.

A 3-pound bag of carrots costs $11.52. What is the price per ounce?

Answers

Answer:

3.75

Step-by-step explanation:

Just divide it in the future!! :)

Answer:

$0.24

Step-by-step explanation:

There are 48 ounces in 3 pounds. Divide 48 by 11.52 to get the unit rate, and the unit rate is $0.24 per ounce

Please hurry please

Answers

Answer:

No

Step-by-step explanation:

it doesn't add up so. No.

Ffind an equation for the tangent to the curve at the given point. Then sketch the curve and the tangent together.

y=8 âx,(1,8)

Answers

Answer:

y = 4x + 4

Step-by-step explanation:

given :

y = 8 [tex]\sqrt{x}[/tex] , (1,8)

The equation for the tangent to the curve at the given point

y' = 8. ( [tex]( \frac{1}{2\sqrt{x} } ) = \frac{4}{\sqrt{x} }[/tex]

next calculate the slope of the tangent (m) = y' at x = 1 = 4

hence the equation of the tangent is

 y - y' = m( x - x1 )

 y - 8 = 4 ( x - 1 )

 y = 4x + 4

attached below is the sketch of the curve and the tangent together

Which term describes the figure? Please help

Answers

Answer:

C . None of these

Is the answer.

Step-by-step explanation:

Because parallel lines do not intersect.

And perpendicular lines form angle of 90°.

Answer:

None of the above.

Step-by-step explanation:

Those lines are intersecting lines. Parallel lines face each other and never meet. Perpendicular lines do meet, but they form a 90 degree angle, which this doesn't. Intersecting lines meet, but don't form a 90 degree angle.

Hope this helps!

please help and I will mark big brain ​

Answers

81, an=-12+((32)-1)3

32-1=31 times 3=93-12=81

Can someone help with this problem? ASAP

Answers

I think it May be b because it’s slope is rising by two

A box on kitty litter is 8 3/4 inches tall. How many boxes can be stacked on a shelf in the warehouse that is 40 inches tall?

Answers

Answer:

Probably about 4 boxes

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