1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
atroni [7]
2 years ago
6

Which of the following represents the zeros of f(x) = x3 − 3x2 − 2x + 6?

Mathematics
2 answers:
Mrac [35]2 years ago
6 0
D. {3, √ 2, -√ 2}. 
<span>The cubic factors- (x - 3)(x² - 2) = 0.</span>
KatRina [158]2 years ago
4 0

Answer:D.) 3, √2, −√2


Step-by-step explanation:

Given polynomial: f(x)=x^3-3x^2-2x+6

Let's check all the given options, by substituting given value on x.

A.) −3, −√2, −√2

f(-3)=(-3)^3-3(-3)^2-2(-3)+6=-27-27+6+6=-42\neq 0

⇒ -3 is not a zero of given polynomial.

Thus, this not the required answer.

B.) 3, −√2, −√2

f(3)=(3)^3-3(3)^2-2(3)+6=27-27-6+6=0

f(-\sqrt{2})=(-\sqrt{2})^3-3(-\sqrt{2})^2-2(-\sqrt{2})+6\\\\=-2\sqrt{2}-6+2\sqrt{2}+6=0

But by Descartes rule of sigs , f(x) have 2 positive and 1 negative root.

Thus, this is not the right answer.

C.) −3, √2, √2

-3 is not a zero of given polynomial.

Thus, this not the required answer.

D.) 3, √2, −√2

f(-3)=(-3)^3-3(-3)^2-2(-3)+6=-27-27+6+6=-42\neq 0

f(\sqrt{2})=(\sqrt{2})^3-3(\sqrt{2})^2-2(\sqrt{2})+6\\\\=2\sqrt{2}-6-2\sqrt{2}+6=0

f(-\sqrt{2})=(-\sqrt{2})^3-3(-\sqrt{2})^2-2(-\sqrt{2})+6\\\\=-2\sqrt{2}-6+2\sqrt{2}+6=0

Thus, this is the right option to have zeroes of f(x).



You might be interested in
-3+3x=-2(x+1)<br> the 2 is a negative<br> please break it down
Veronika [31]
-3+3x=-2(x+1) First: I will get rid of the bracket:


-3+3x=-2x-2

Now, all the x goes to the left side, all the numbers without x to the right side:


3x+2x=-2+3

we add up"

5x=1

divide by 5:

x= \frac{1}{5}

7 0
3 years ago
Read 2 more answers
An excursion group of four is to be drawn from among 5 boys and 6 girls.
tresset_1 [31]

Answer:

Because you are recounting people several times. Say for example, let us number those people

{1,2,3,4} for the four girls and {1,2…7} for the boys.

One possible combination by your way is to fix one boy and girl each, say

{1,1} and then choose the remaining people. Let this combination be, for the sake of the example, {1,1,2,2,3}. This is a valid combination.

Now, when you fix another combination of a boy and a girl, say {1,2}, you could get the same combination as before because one the combinations while choosing the three remaining people would be {1,2,3}.

A correct way would be to choose  girls and then choose 5− boys for 1≤≤4

So we get ∑4=1(4)(75−)=441

5 0
3 years ago
Read 2 more answers
Write the equation of a parabola with a vertex and (-5, 2) and a directrix y = -1
mrs_skeptik [129]

Answer:

y=(x+5)²/6 + 1/3

Step-by-step explanation:

Use the distance formula to plug in the values you know:

√(y+1)² =√(x+5)² +( y-2)²

the square roots cancel out

(y+1) ²= (x+5)² +(y-2)²

(y+1) (y-1)= (x+5)² + (y-2) (y-2)

y²+2y+1= (x+5)² + y² -4y+4

the y² cancel out

2y+ 4y = (x+5)² + 4-1

6y= (x+5)² +3

y= (x+5)² /6+ 1/3

4 0
3 years ago
Suppose that a butterfly can fly 82 feet in 4 seconds. A dragonfly can fly 50 feet in 2 seconds. Which can fly faster and by how
Lady bird [3.3K]

A butterfly can fly 82 feet in 4 seconds.

Distance traveled by butterfly = 82 feet.

Time taken by butterfly =4 seconds

Speed = distance /time

Speed of butterfly = 82/4 = 20.5 feet/second

A dragonfly can fly 50 feet in 2 seconds.

Distance traveled by dragonfly =50 feet.

Time taken by dragonfly =2 seconds.

Speed of dragonfly = 50/2 = 25 feet/second

So dragonfly can fly faster than the butterfly.

Difference in speed = speed of dragonfly - speed of butterfly = 25-20.5 = 4.5

So The dragonfly is 4.5 feet per second faster than butterfly.

Answer: B) The dragonfly is 4.5 feet per second faster.  


5 0
3 years ago
Read 2 more answers
Pleaseeeeeeeeeee help meeeeee
Aloiza [94]
The answer is c thank me later
4 0
2 years ago
Other questions:
  • What is the length of MN?
    14·2 answers
  • PLEASE HELP, I need to get this assignment done soon
    13·1 answer
  • Answer this please! This is a lightshot/picture please answer and you shall be greeted with 10PTS!!
    15·1 answer
  • PLEASE HELP ITS DUE TODAY!!!Mr.Sanchez's Class sold fruit pues for $1.65 and Mr.Kellys class sold bottles of fruit juice for $1.
    14·1 answer
  • Find the slope and y-intercept from the following graph of a linear equation.
    9·1 answer
  • Solve for a.
    11·2 answers
  • The price of a pair of shoes is $52. The price is 15% lower than last week.
    14·2 answers
  • Can u pls help me with this question asap​
    12·1 answer
  • A rectangle has length (3x+5) cm and width (2x - 1) cm. What is the area of the<br> rectangle?
    10·1 answer
  • Rena`s rowboat drifts 23 feet away from the shore, followed by another 9 more feet. What equation represents Rena`s rowboat posi
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!