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
xeze [42]
3 years ago
14

Find the real zeros of f(x); there are 4 zeros

Mathematics
2 answers:
lora16 [44]3 years ago
8 0

Answer:

[x - 4][x + 2][2x + 3][x - 1]; 1, -2, -1\frac{1}{2}, 4 = x

Step-by-step explanation:

By the Rational Root Theorem, we take the Least Common Divisor [LCD] between the <em>leading coefficient</em> of 2, and the <em>initial value</em> of 24, which is 1, so this automatically makes our first factor of x - 1. Next, since the factor\divisor is in the form of x - c, use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

1| 2 −3 −21 −2 24

↓ 2 −1 −22 −24

_______________

2 −1 −22 −24 0 → 2x^3 - x^2 - 22x - 24

You start by placing the <em>c</em> in the top left corner, then list all the coefficients of your dividend [2x⁴ - 3x³ - 21x² - 2x + 24]. You bring down the original term closest to <em>c</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 2 in your quotient can be a 2x³, the −x² follows right behind it, bringing −22x right up against it, and bringing up the rear, −24, giving you the quotient of 2x^3 - x^2 - 22x - 24.

However, we are not finished yet. This is our <em>first quotient</em>. The next step, while still using the Rational Root Theorem with our <em>first</em><em> </em><em>quotient</em>, is to take the Greatest Common Divisor [GCD] of the <em>leading coefficient</em> of 2, and the <em>initial value</em> of −24, which in this case would be −2 because the negative overpowers everything, so this makes our next factor of x + 2. Then again, we use Synthetic Division because x + 2is in the form of x - c:

−2| 2 −1 −22 −24

↓ −4 10 24

____________

2 −5 −12 0 → 2x^2 - 5x - 12

Finally, you can just simply factor this second quotient:

2x^2 - 5x - 12 \\ \\ [2x^2 + 3x] - [8x - 12] \\ x[2x + 3] \: \: -4[2x + 3] \\ \\ [x - 4][2x + 3]

So altogether, we have our four factors of [x - 4][x + 2][2x + 3][x - 1], then setting all factors equal to zero, you get all the values of 1, -2, -1\frac{1}{2}, and\:4.

I can assist whenever I can.

ziro4ka [17]3 years ago
7 0

Answer:

x = 4 or x = 1 or x = -2 or x = -3/2

Step-by-step explanation:

Solve for x over the real numbers:

2 x^4 - 3 x^3 - 21 x^2 - 2 x + 24 = 0

The left hand side factors into a product with four terms:

(x - 4) (x - 1) (x + 2) (2 x + 3) = 0

Split into four equations:

x - 4 = 0 or x - 1 = 0 or x + 2 = 0 or 2 x + 3 = 0

Add 4 to both sides:

x = 4 or x - 1 = 0 or x + 2 = 0 or 2 x + 3 = 0

Add 1 to both sides:

x = 4 or x = 1 or x + 2 = 0 or 2 x + 3 = 0

Subtract 2 from both sides:

x = 4 or x = 1 or x = -2 or 2 x + 3 = 0

Subtract 3 from both sides:

x = 4 or x = 1 or x = -2 or 2 x = -3

Divide both sides by 2:

Answer:  x = 4 or x = 1 or x = -2 or x = -3/2

You might be interested in
Mark and don are planning to sell each of their marble collections at a garage sale. if don has 2 more than 4 times the number o
Sonbull [250]

If the total number of marbles is 102, Mark has 20 marbles while Don has 82 marbles.

To answer this word problem, read and understand first the problem.

"Don has 2 more than 4 times the number of marbles Mark has."

Out of this statement, we can come up with the expression,

Don = 2 + (4 x Mark)     (equation 1)

Next, the total number of marbles they have is 102.

Don + Mark = 102     (equation 2)

From this expression, if we subtract the number of marbles Mark has from the total number, we can get the number of marbles Don has.

Don = 102 - Mark    (equation 3)

Equating the 1st and 3rd equation,

Don = 2 + (4 x Mark) = 102 - Mark

2 + (4 x Mark) = 102 - Mark

let x = Mark's

2 + (4x) = 102 - x

4x + x = 102 - 2

5x = 100

x = 20

Mark has 20 marbles.

Meanwhile, use either the 1st or 3rd equation to know the number of marbles Don has.

Don = 102 - Mark    (equation 3)

Don = 102 - 20

Don = 82

For more examples of mathematical expressions to solve word problems:, brainly.com/question/13818690.

#SPJ4

7 0
1 year ago
What are the solutions to the equation -54 + 6x = 0
Sladkaya [172]

Answer:

x=9

Step-by-step explanation:

  1. -54 + 6x  =   6 • (x - 9)
  2. Solve :    6   =  0
  3.  Solve  :    x-9 = 0
  4. Add  9  to both sides of the equation :     x = 9
7 0
3 years ago
Read 2 more answers
In a school of 685 students, there are 385 students involved in sports teams, and there are
svet-max [94.6K]

Answer:

A) check attached picture

B) 272

C) 0.4478

Step-by-step explanation:

From the information given ;

A) The Venn diagram of the information can be found in the attached picture.

B) Number of students involved in both team sports and music.

n(student in sports team) = 385

n(students involved in music) = 450

Number of students involved in both music and team sport = y

Number of students not involved in either team sport or music = 87

Total number of students = 650

Therefore,

n(music alone) = 450 - y

n(team sport alone) = 385 - y

Adding the following:

n(music alone) + n(team sport alone) + n( both music and team sport) + n(neither music nor team sport) = Total number of students

450 - y + 385 - y + y + 87 = 650

922 - y = 650

922 - 650 = y

y = 272

Therefore, number of students involved in both music and team sport = 272

C) probability of being involved in team sport or in music.

P(being involved in music) = (450 - 272) / 650 = 0.2738

P(being involved in team sport) = (385 - 272) / 650 = 0.1738

P(involved in both) = 272 / 650 = 0.4184

P(involved in neither) = 87 / 650 = 0.1338

P(being involved in team sport) or p(being involved in music)

P(being involved in team sport) + p(being involved in music)

0.1738 + 0.2738 = 0.4478

3 0
3 years ago
If you answer both I will give Brainliest they have to be correct.Good luck
svetlana [45]

Answer:

3

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Find the next three terms of each geometric sequences. 4,8,16_,_,_
alekssr [168]
32 64 128 are the answers
5 0
2 years ago
Other questions:
  • Divide. Write your answer as a fraction in simplest form. 9/10÷(−6/5)=
    15·1 answer
  • If 60% of a number is 144 what is the number?
    12·1 answer
  • Select the correct answer.
    8·1 answer
  • Find the exact value of <br> sin−1−32
    10·1 answer
  • A car travels 240 miles in 3 hours and 45 minutes. How many miles does it travel per hour?
    10·1 answer
  • Which statement about the slope of the line is true?
    13·1 answer
  • Help help math suckssss
    12·1 answer
  • Select all of the choices that are equivalent to 2 to the power of 3. is what i put right?
    11·1 answer
  • Mathematics question
    12·2 answers
  • Find the circumference of the circle. area = 121pi ft2
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!