HELPPPPP
Which of the following are roots of the polynomial function below?
Check all that apply.
F(x) = x^3 -3x²+2
Answers
The roots of the polynomial function f(x) = x³ - 3x² + 2 are [tex]\frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}, \ and \ 1[/tex].
What are the roots of the polynomial function?Given the polynomial function in the question:
f(x) = x³ - 3x² + 2
To find the roots of the polynomial function f(x) = x³ - 3x² + 2, we need to solve for values of x that make the function equal to zero.
f(x) = x³ - 3x² + 2
x³ - 3x² + 2 = 0
Factor the equation using the rational root test:
( x - 1 )( x² - 2x - 2 ) = 0
Equate each factor zero and solve for x:
( x - 1 ) = 0
x - 1 = 0
x = 1
( x² - 2x - 2 ) = 0
x² - 2x - 2 = 0
Using the quadratic formula:
[tex]x = \frac{-b\±\sqrt{b^2 - 4(ac)} }{2a} \\\\x = \frac{-(-2)\±\sqrt{(-2)^2 - 4(1*-2)} }{2*1} \\\\x = \frac{2\±\sqrt{4 + 8} }{2} \\\\x = \frac{2\±\sqrt{12} }{2}\\\\Hence:\\\\x = \frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}[/tex]
Therefore, the roots are [tex]x = \frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}, 1[/tex].
Options A, B and D are the correct answers.
Learn more about quadratic equations here: brainly.com/question/1863222
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Related Questions
Does anyone know how to solve this?
Answers
Answer:
first car : 115 liters
second car: 135 liters
Answer:
car 1 = 173.08 liters
car 2 = 76.92 liters
Step-by-step explanation:
the first step is to find what ratio of car 1 is to car 2
that is 18:8
total ratio is 26
the combination of car 1 and 2 = 26
the total km = 3350
total fuel = 250 liters
car 1 = 18 x 250 liters
26
= 173.08 liters
car 2 = 8 x 250 liters
26
= 76.92 liters
173.08 + 76.92 = 250
Which of the following sets include all rational numbers?
Answers
It's the Second one and the third one
Step-by-step explanation:
Pie is irrational so you can easily cross it off and it leads to to the second one and the third one
This recipe makes 7 pancakes.
Sanjay follows the recipe but wants to make 21 pancakes.
How much of each ingredient does he need?
Recipe: Makes 7
135 g flour
1 teaspoon (tsp) baking powder
2 tablespoons (tbsps) sugar
130 ml milk
1 egg
Answers
Answer:
he needs 3 times all the 1 to make 21 pancakes
Step-by-step explanation:
Liz wants to buy a shirt for $25.what will the total cost after tax be if Liz buys the shirt in Springfield
Answers
Answer:
ya
Step-by-step explanation:
P= 2.50n - 300
How many candy bars must be sold to make a profit of $500?
Answers
Answer:
I need the answer
I dont know!!
Step-by-step explanation:
Help needed. 30 points to complete the table and do the second part.
Answers
Answer:
-4,-6,-8,-10
Step-by-step explanation:
I am not so sure though.
Megan drew a fraction that shows 6/8. What number can divide both the numerator and denominator to simplify this fraction?
Answers
Answer:
2Step-by-step explanation:
The required number is 2. This divides 6 into 3 and 8 into 4. The simplified fraction is 3/4, which cannot be further simplified.
HELP ASAP!!
Solve the following quadratic equation for all values of x in simplest form.
3(x - 2)2 – 37 = 20
Answers
pls give brainliest if you found my answer helpful
Work: Step 1) 3(x-2)2-37=20
Step 2) (3x-6)2-37=20
Step 3) 6x-12-37=20
Step 4) 6x-12= 20+37
Step 5) 6x=57+12
Step 6) 6x=69
Step 7) x=69/6
Step 8) x= 23/2
H E L P PLZZZ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
138
Step-by-step explanation:
just plug in the numbers:
4*6^2 - 36/6
use pemdas
4*36 - 6 = 144-6 = 138
Answer: The answer is 138.
Step-by-step explanation: First, find 6 squared. That is 36. Multiply that by 4 to get 144. After that, find 36 divided by 6. That is 6. Finally, subtract 144 and 6.
If a = 3 sqrt(3) in the right triangle shown, what is the value of b?
Answers
Note: Consider the below figure attached with this question.
Given:
[tex]a=3\sqrt{3}[/tex]
To find:
The value of b.
Solution:
In a right angled triangle,
[tex]\tan \theta = \dfrac{Perpendicular}{Base}[/tex]
For the given right angled triangle,
[tex]\tan \theta = \dfrac{a}{b}[/tex]
[tex]\tan (30^\circ) = \dfrac{3\sqrt{3}}{b}[/tex]
[tex]\dfrac{1}{\sqrt{3}} = \dfrac{3\sqrt{3}}{b}[/tex]
On cross multiplication, we get
[tex]1\times b=3\sqrt{3}\times \sqrt{3}[/tex]
[tex]b=3(3)[/tex]
[tex]b=9[/tex]
Therefore, the value of b is 9.
What is the opposite operation of the square root?
Answers
Answer:
The opposite of multiplication is division. The opposite of division is multiplication. The opposite of taking a square root is squaring
Step-by-step explanation:
How many boxes of tissue can you buy with $21 if one box costs $7?
Answers
Answer: 3 boxes
Step-by-step explanation: Divide 21 and 7.
Karen performs a transformation on parallelogram ABCD that is plotted on a coordinate grid to form parallelogram A'B'C'D'. The image of
each point is shown in the table below.
Image
Original
Point
| A(-4,-1)
B (-7,-6)
C (-14, -6)
D(-11, -1)
(1.-4)
(6.-7)
(6.-14)
(1.-11)
Which best describes the transformation Karen performed?
A.reflection over the y-axis
B.dilation of scale factor
-1/4
C.counterclockwise rotation of 90 degrees about origin
D.translation of 5 units to the right and 3 units down
Answers
Answer:
its c
Step-by-step explanation:
took the test
Karen performed a transformation of (C) counterclockwise rotation of 90 degrees about origin
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is rotated 90° counterclockwise about the origin, the new point is at A'(-y, x).
Parallelogram ABCD has vertices at A(-4,-1) , B (-7,-6) , C (-14, -6) , D(-11, -1), if it is rotated 90° counterclockwise about the origin, the new point would be at A'(1.-4) , B'(6.-7), C'(6.-14) , D'(1.-11)
Find out more at: https://brainly.com/question/11707700
Given the conditional statement: "If it is Wednesday, then Kayden doesn't
have baseball practice." What is the hypothesis of this statement? *
Answers
Answer:
if it's wednesday
Step-by-step explanation:
PLEASE HELP FAST ILL GIVE BRAINLIST MAKE SURE YOU READ IT BEFORE YOU ANSWER ITS QUESTION 18
Answers
Answer:
D. y=3x+15
Step-by-step explanation:
find the slope
[tex]\frac{1-(-5)}{-3-(-1)} =3[/tex]
y=mx+b
plug in known values
3=3(-4) + b
b=15
y=3x+15
This table gives the minutes players spent practicing basketball free throws and the number of baskets they made when they were timed the next day at practice.
Practice time (min) 45 100 57 8 90 63 25 84 30 120 19 18
Baskets made 15 21 18 5 22 18 19 23 16 20 7 10
What is the correlation coefficient of the data?
0.12
0.64
0.80
0.92
Answers
Answer:
0.79769, or 0.80 if you round it up
Step-by-step explanation:
A department store sells a pair of shoes with an 87% markup. If the store-bought
the pair of shoes for $55.25, what is the selling price to the nearest dollar?
Answers
Answer:
Step-by-step explanation:
55.25x.87=48.07
55.25+48.07=103.32
How many x-intercepts would the function shown below have? F(x)=-5(x^2-7)(x+6)^2(x+1)(4x+1)
Answers
Answer:
5
Step-by-step explanation:
plug this ecuation into desmos graphing calculator(it's a website). Then see how many times the graph crosses the x-axis.
To find the zeroes:
0 of a function means for what value(s) of x will the f(x) or y equal zero(0). To find the zeroes of this function, just see what numbers will make f(x) = 0. Since this equation is already factored, our job is much easier. Focus on small parts of the equation and don't get ovewhelmed by how long it its. For you problem, start by -5(x^2-7). what x will make -5(x^2-7) = 0? As long as (x^2-7) = 0, the whole equation will equal zero since any number times 0 is 0. (x^2-7)=0, move -7 to the right, x^2=7, get squre root of both sides, you will have x=plus or minus[tex]\sqrt{7}[/tex]. This is one of the zeroes. There are many more in this equation since we have more than one x-intercepts. Now using thsi tactic, you can solve for the rest of the zeroes.
there is a calculator called symbolab, It's also a website and it can calculate whatever you need.
The number of x-intercepts is five would be the given function.
What is x-Intercept?The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses,
The function is given in the question
F(x) = -5(x²-7)(x+6)²(x+1)(4x+1)
We have to determine the number of x-intercepts that would the function.
F(x) = -5(x²-7)(x+6)²(x+1)(4x+1)
The x-intercept occurs at a point where F(x) = 0
0 = -5(x²-7)(x+6)²(x+1)(4x+1)
-5(x²-7)(x+6)²(x+1)(4x+1) = 0
Here (x²-7) = 0, and (x+6)² = 0, (x+1) = 0, and (4x+1) = 0
x² = 7 , and (x+6) = 0, x = -1 , and 4x = -1
x = ±7 and x = -6 , x = -1 , and x = -1/4
x = 7, -7 and x = -6 , x = -1 , and x = -1/4
Therefore, the number of x-intercepts is five would be the given function.
Learn more about the x-intercept here:
https://brainly.com/question/14180189
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632 16/25 + 31 3/10 and turn it into a decimal :)
Answers
Answer:
663.94
Step-by-step explanation:
Can someone help me please
Answers
Answer:
17 inches
Step-by-step explanation:
NEED HELP ASAP!
Tank A contains 35 gallons of water and is increasing at a rate of 5 gallons per minute. TankB
contains 100 gallons of water and is decreasing at a rate of 8 gallons per minute. In how
many minutes will the tanks contain the same amount of water? How much water will
that be?
Answers
9514 1404 393
Answer:
5 minutes; 60 gallons
Step-by-step explanation:
The volume in tank A is initially 35 gallons. Its rate of change is 5 gallons per minute. The equation for volume can be written as ...
y = 35 +5x . . . . . . where y is gallons, and x is minutes
The volume in tank B is initially 100 gallons. Its rate of change is -8 gallons per minute. The equation for volume can be written as ...
y = 100 -8x
We want to find the values of x and y such that both are the same for both tanks.
35 +5x = y = 100 -8x
13x = 65 . . . . . . . . add 8x-65 to both sides of the equation
x = 5
y = 100 -8·5 = 60
Both tanks will hold 60 gallons after 5 minutes.
help please i’m stuck lol
Answers
Answer:
The answer for this is x=-5
Answer:
x=-5
Step-by-step explanation:
-4x+1=21
move the 1 to the right side and subract it so it will turn into -4x=20
divide -4 to get the x by itself and then you will get x=20/-4 this will now divide and be x=-5
5.
Select the correct answer from each drop-down menu.
A school club will be competing at a state championship has been working to raise money for the club's travel expenses. The table shows
the amount of money raised each month over a nine-month period beginning in August
Month
1
2
4
5
6
7
8
9
Amount ($)
250
275
325
300
350
375
375
350
350
Based on the data in the table, Clara and Michael each use their own function to determine the amount of money the club should expect to raise
in the next three months.
Clara's function: y = -3.14.2 + 44.75 + 203.6
Michael's function: y = 44.64V1 + 1 + 246.5
How does using the different models affect the amount of money the club would expect to raise in the next three months?
If the club uses Clara's function, it would expect the amount of money to
If the club uses Michael's function, it would expect the amount of money to
each month
each month
Reset
Next
Answers
Answer:
descrease & increase
Step-by-step explanation:
Answer:
Decrease and increase.
Step-by-step explanation:
Solve for x:2/5 (x - 2) = 4x
Answers
Answer:
x= -2/9
Step-by-step explanation:
2(x-2)/5=4x
2(x-2)=4x*5
2(x-2)=20x
x-2=20x/2
x-2=10x
-2=10x-x
9x= -2
x= -2/9
Find the missing term: 1, 1.5, x, 2.5, 3,
Answers
Answer:
x=2
Step-by-step explanation:
Counting by 0.5 pattern
--- BONUS!---
During one night, possums ate two fifths of the fifty five fruits on a tree. If one eleventh of the
eaten fruit grew back, how many fruits are now on the tree?
Grade 8 Number Sense and Numeration
IL
Answers
Answer:
35
Step-by-step explanation:
2/5x55=22
55-22=33
22x1/11=2
33+2=35
35 left on tree
Plsssss helppp meeeeee
Answers
Answer:
First choice, 1/3
Step-by-step explanation:
If you look at 1 to A to B to 2, you would see that there are 3 gaps between them. Therefore it's out of three, A to B is only one gap distance so it's 1/3
The answer is 1/3.
- emmatannerfns
The area of a rectangle is 15 square inches. What wil be the area, in square inches, of the rectangle after it is dilated by a
scale factor of 2?
Answers
Answer:
60 inches²
Step-by-step explanation:
Unit test
1 Ray is making a dessert by mixing honey and yogurt in the ratio of 2 to 13. How much yogurt and honey does he need to ma 600 grams of the dessert
Answers
Answer:
80 grams honey, 520 grams yogurt
Someone help!
Three customers have accounts owing money. The table shows the account balances.
Which customer owes the least amount of money?
Customer Balance
M. Palmer –$56.72
B. Leftwich –$74.19
R. Jordan –$54.31
M. Palmer
B. Leftwich
R. Jordan
Answers
jordan owes the least amount of money