The polynomial n(x) = 3x4 - 9x3 + x2 – 3x has a factor of (x – 3).
Complete each of the 2 activities for this Task.
Activity 1 of 2
Part A: State the number of roots of the polynomial n(x).
A. 2 real roots; 2 complex roots
B. 4 real roots
O C. 3 real roots; 1 complex root
0
D. 1 real root; 3 complex roots
Answers
Answer:
Step-by-step explanation:
2 real roots and 2 complex
Following are the solution to the given polynomial equation:
Given:
Polynomial equation: [tex]\bold{n(x) = 3x^4 - 9x^3 + x^2 -3x}[/tex]
Factor: [tex]\bold{(x -3)}[/tex]
To find:
A number of roots for the polynomial n(x).
Solution:
Polynomial equation: [tex]\bold{n(x) = 3x^4 - 9x^3 + x^2 -3x}[/tex]
[tex]\to \bold{(x -3)=0}\\\\\to \bold{x =3}\\\\[/tex]
Putting the of x into the given Polynomial function:
[tex]\to \bold{n(3) = 3(3)^4 - 9(3)^3 + (3)^2 -3(3)}\\\\\to \bold{n(3) = 3\times 81 - 9\times 27 + 9 -3 \times 3}\\\\\to \bold{n(3) = 243- 243 + 9 -9}\\\\\to \bold{n(3) = 0}\\\\[/tex]
Let divide the Polynomial function by the factor:
[tex]\to \bold{\frac{3x^4 - 9x^3 + x^2 - 3x}{x-3}}\\\\\to \bold{\frac{ x(3x^3 - 9x^2 + x - 3)}{x-3}}\\\\\to \bold{\frac{ x(3x^2(x - 3)+1(x - 3))}{x-3}}\\\\\to \bold{\frac{ x(x - 3) (3x^2+1)}{x-3}}\\\\\to \bold{x(3x^2+1)}\\\\[/tex]
So, the factors are [tex]\bold{x, (x-3),\ and \ (3x^2+1)}[/tex].
Calculation of the roots:
[tex]\bold{x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ x-3=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3x^2+1 =0}\\\\\bold{x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ x=3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3x^2 = -1}\\\\\bold{x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ x=3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x^2 = -\frac{1}{3}}\\\\\bold{x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ x=3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x^2 = (- \sqrt{\frac{1}{3}})^2}\\\\[/tex]
Therefore the final answer is "Option A".
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Related Questions
PLEASE HELP WILL GIVE BRAINLIEST TO CORRECT ANSWER
Answers
Answer:
Step-by-step explanation:
h(x) = 7 - x - 2x^5
h(-1) = 7 + 1 - 2(-1)^5
h(-1) = 7 + 1 + 2
h(-1) = 10
Now differentiate h(x)
h'(x) = -1 - 2*5*x^4
h'(x) = -1 - 10x^4
h'(x) = -1 - 10(x)^4
h'(x) = -1 - 10 (x)^4
h'(-1) = -1 - 10(10000)
h'(-1) = -1 - 100000
h'(-1) = - 99999
A city council organized a marathon race to promote good health. There were 3 times as many female participants as male participants in the marathon. If the total number of participants was 812, how many participants were male
Answers
Answer:
609 males
Step-by-step explanation:
A city council organized a marathon race to promote good health.
Let the number of
Females = x
Males = y
There were 3 times as many female participants as male participants in the marathon.
3x = y
If the total number of participants was 812,
x + y = 812..... Equation 1
We substitute 3x for y in Equation 1
x + 3x = 812
4x = 812
x= 812/4
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3(203) = 609 males
The number of males participants = 609
The sum of three numbers is 107 . The first number is 8 less than the third . The second number is 3 times the third . What are the numbers ?
Answers
Third number = x - 7
Second number = 2(x - 7)
x + 2(x - 7) + x - 7 = 107
x + 2x - 14 + x - 7 = 107
Collect like terms.
4x - 21 = 107
4x = 128
x = 32
First number = 32
Second number = 50
Third number = 25
Total = 107.
Answer:
(x - 8) + 3x + x = 107
x - 8 + 3x + x = 107
5x - 8 = 107
5x = 115
x = 23, SO...
The first number is 23-8, which is 15
The second number is 3 x 23, which is 69
The third number is 23
15 + 69 + 23 = 107 CHECK!
Step-by-step explanation:
BC has endpoints B(-3,-5) and C(12,12). FInd the coordinates of the midpoint of BC
Answers
Answer:
(9/2, 7/2)
Step-by-step explanation:
The easiest way to remember how to do this problem is to average the x-coordinates and average the y-coordinates.
So, in your problem (-3 + 12)/2 = 9/2 and (-5 + 12)/2 = 7/2
The midpoint is (9/2, 7/2)
4x+14+8x-14=180 find for x
Answers
4x + 14 + 8x -14 = 180
Add/subtract x terms and non x terms
12x = 180
x = 180/12 = 15
Check if answer is right by putting x = 15 back into original equation and seeing if it equals 180
4(15) + 14 + 8(15) -14 = 180
Answer is correct.
this time I cannot tell what the answer is
Answers
Answer:
Its the first one
Step-by-step explanation:
27 ÷ 3 and 3 ÷ 27
associative property
Yes, commutative property
Yes, identity property
No, they are not equal
which one is it
Answers
Answer:
No they aren't equal........
In a financial crisis, the number of bankruptcies will likely be ____ and the company profits will likely be O A. larger; larger O B. smaller; smaller C. smaller; larger O ; D. larger; smaller
Answers
Answer:larger ,smaller
Step-by-step explanation:
Answer:
larger, smaller
Step-by-step explanation:
on aoex
what is the solution of the exponential equation? use a graph. full calculations,[tex]27=3^{x-2}[/tex] please!!
Answers
Answer:
5
Step-by-step explanation:
if i really need to use a graph leave a comment
27=3ˣ⁻²
[tex]x=y^z\\=\\log_{y}x=z\\[/tex]
Which means that
[tex]27=3^{x-2}=\\log_327=x-2\\log_327=\frac{log27}{log3}=3\\3=x-2\\x=5[/tex]
Which of the following is a solution of x2 + 4x + 6? (1 point)
Answers
Answer:
I LOVE ALGEBRA anyways
othe ans is in the picture and the steps how got the ans
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Step-by-step explanation:
Using the slope formula, find the slope of the line through the given points.
(6,6) and (8,2) what is the slope line
Answers
Answer:
-2
Step-by-step explanation:
To do this you just have to do the slope formula which is y2-y1/x2-x1 then plug in the numbers so you get 2-6/8-6 which would get you which can be reduced to -2 so that would be the answer
Its not a quiz/test its homework thats due in a bit :)
Just to clear any misunderstandings that might arise
Answers
Answer:
MN = 25
Step-by-step explanation:
If LN=45, then the addition of both quantities will be 45.
LN = 3x + 2 + x + 19
3x + 2 + x + 19 = 45
4x + 21 = 45
4x = 45 - 21 = 24
x = 6
Now that we found the value of "x", we can find the lenght of MN
MN = x + 19
MN = 6 + 19
MN = 25
Hope it was helpful ;)
Answer: MN = 25
Step-by-step explanation:
Since the length is already given we just add the equations equal to it.
45 = 3x + 2 + x + 19 Combine like terms
45 = 4x + 21 Subtract 21 from both sides
24 = 4x Divide by 4
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Now we plug x into the equation needed.
X + 19
6 + 19 = 25
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Answers
In your own words explain how you would solve this two step equation for the variable x. 9x-7=-7
Answers
Answer:
Add 7 to both sides
Step-by-step explanation:
The equation has to be just x = y
There cannot be another number on the same side as the variable
Now that we did that, the equation is 9x = 0
x = 0
Well, that was easy lol
Answer:
Step-by-step explanation:
Add 7 to both sides
9x = 0
Then divide by 9 both sides to get x by itself
x = 0
A rectangular garden is to cover 416 square feet of area. If the width is 10
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Answers
Answer:
Length = 26 feet, Width = 16 feet
Step-by-step explanation:
Let the length be l.
Width b = l-10
The area of a rectangular garden, A = 416 feet²
We need to find the dimensions of the garden. The area of a rectangular shaped object is given by :
[tex]A=lb\\\\l(l-10)=416\\\\l^2-10l-416=0\\\\l=26\ ft,-16\ ft[/tex]
Neglecting the negative value, the length of the garden is 26 feet and the width is 12-10 = 16 feet.
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Answers
Answer:
486,585
Step-by-step explanation:
x = total number of books sold
0.082 x x = 39,900
to find x divide both sides by 0.082
x = 486,585
7 pink flowers, 9 purple flowers, and 5 white flowers. What is the ratio of purple flowers to total flowers?
Answers
Answer:
9:21
Step-by-step explanation:
Answer:
9:12
Step-by-step explanation:
There are 9 purple flowers, 7 pink flowers, and 5 white flowers.
If you want the ratio of purple to the total, all you have to do is add the pink and white flowers together.
So the answer would be...
9:12
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Answers
Answer:
− 7 ⋅ a
Step-by-step explanation:
Nothing further can be done with this topic. Please check the expression entered or try another topic.
Answer:
a = -2
Step-by-step explanation:
-7 * -2 = 14
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Answers
Answer:
2/9
Step-by-step explanation:
Total cones sild= 72
Pistachio ice cream sild= 16
p= 16/72
p=2/9
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Answer:
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Step-by-step explanation:
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Answer:
If the game will start at 11:00 A.M., but the players must arrive at the field three-quarters of an hour early to warm up, it refers to 8:45 a.m. Why? If we start to count in 11 backward and start to trace the three-quarters, it shows that 10:45, 9:45, and 8:45 are the three-quarters. So Hamid statement that he has to be at the field at 9:45 A.M is not correct.
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
x=120 (x-60)=60
Step-by-step explanation:
Because the unlabeled angle and right angle are parallel we can assume that the unlabeled angle will be 90 degrees.
90+90+x+(x-60)=360
120+2x=360
-120 -120
2x=240
x=120
(x-60)
120-60
60
Evaluate the expression.
-8.x – 3y if x = 4 and y = -2
Answers
Answer:
-8.4 + 6 hope this helped!
Step-by-step explanation:
Answer:
-38
Step-by-step explanation:
-8.x – 3y
x = 4
y = -2
Since we have the value for x and y we can use that and substitute it into the expression
-8(4) - 3 (-2)
-32 - 6
When you add 2 negative numbers (or subtract them) they will give you a bigger number so think of it as adding 2 positive numeber, but then putting a negative sign in the beginning of it.
-32 - 6
-38
Hope this helped!
Have a supercalifragilisticexpialidocious day!
Luisa found great deals on the target dollar spot. She bought 35 items and spent a total of $100 on earbuds ($2 each) and fuzzysocks ($3 each). How many earbuds did she buy? how many fuzzy socks did she buy?
Answers
Answer:
50 earbuds because
Step-by-step explanation:
half of 100 is 50
Answer:
x=35 earbuds
Step-by-step explanation:
The following histogram summarizes the ages of the 25 employees who work for Elon's company. According to the 1.5 IQR wall for outliers how many high outliers are there in the data set
Answers
Answer:
Step-by-step explanation:
1
The number of high outliers in the data set will be 1.
What is the interquartile range?The interquartile range is a measurement of a data set's "middle fifty." A range is a measurement of where a set's beginning and end are located.
To get the interquartile range, we must know the first and third quartiles. To find those, we need to know the median of the data.
The following histogram summarizes the ages of the 25 employees who work for Elon's company. According to the 1.5 IQR wall for outliers. The number of the high outliers will be 1.
Therefore, the number of high outliers in the data set will be 1.
To know more about the interquartile range follow
https://brainly.com/question/4102829
#SPJ2
Simplify the following expressions and evaluate any numerical expressions.
(−3x)2
Select one:
−9x4
−9x2
9x4
9x2
Answers
Answer:
-6x
Step-by-step explanation:
Why is it 9? Cuz its not 3(3)
help with rounding off!!please
Answers
Answer:
Step-by-step explanation:
A.0.4821 ( 3 d.p)=0.482
B.0.595 (2 d.p)= 0.60
C.0.0346(3 d.p)=0.03
D.2.94999(1 d.p)=2.9
Mark me as a brainliest
0.60
0.03
2.9
those are the answers
When solving the inequality 3x - 2 < 8x + 10, the next line
becomes 3x < 8x + 12. Which property justifies this step?
(1) Distributive
(2) Associative
(3) Multiplicative Property of Equality
(4) Additive Property of Equality
Answers
Cone A has a diameter of 12 meters and a slant height of 9 meters. The linear dimensions of cone B are 5 times the linear dimensions of cone A. Compare the volume of cone B to the volume of cone A.
******ill give brainliest plz help me*****
Answers
Answer:
Cone volume formula
To calculate its volume you need to multiply the base area (area of a circle: π * r²) by height and by 1/3: volume = (1/3) * π * r² * h
Step-by-step explanation:
Distribute and solve
(p + 24) = 9
Answers
Answer:
p+24=9
p=-15
Step-by-step explanation:
plz make me brainliest
p + 24 = 9
-24 = -24
p = -15