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
Morgarella [4.7K]
3 years ago
6

one factor of f(c) = 5x3 + 5x2 - 170x + 280 is (x + 7). What are all the roots of the function? Use the remainder theorem

Mathematics
2 answers:
MAXImum [283]3 years ago
5 0

Answer:

Roots of the f(x) is -7 , 4 and 2.

Step-by-step explanation:

Given:

f(x)=5x^3 +5x^2-170x+280

One factor of f(x) = x + 7

⇒ One root , x = -7

To find: All roots of the function Using Remainder theorem.

First we find All factors of the given f(x).

On dividing f(x) by given factor we get,

f(x) = ( x + 7 ) ( 5x² - 30x + 40 )

     = ( x + 7 ) ( 5x² - 20x - 10x + 40 )

     = ( x + 7 ) ( 5x( x - 4 ) - 10( x - 40 ) )

     = ( x + 7 ) ( x - 4 ) ( 5x - 10 )

Remainder Theorem: Remainder theorem states that if a polynomial p(x) is divided by a linear polynomial of form x -a then remainder is given by p(a).

Put x = -7 in the given function,

f(-7) = 5(-7)³ + 5(-7)² - 170(-7) + 280 = -1715 + 245 + 1190 + 280 = 0

So, First root is -7

Now, Put x = 4

f(4) = 5(4)³ + 5(4)² - 170(4) + 280 = 320 + 80 - 680 + 280 = 0

So, Second root is 4

Now put x = 10/5 = 2

f(2) = 5(2)³ + 5(2)² - 170(2) + 280 = 40 + 20 - 340 + 280 = 0

So, Third root is 2

Therefore, Roots of the f(x) is -7 , 4 and 2.

elena55 [62]3 years ago
4 0

Answer:

So the roots of the polynomial are -7 , 4 , 2

Step-by-step explanation:

Given the polynomial in the question

5x³ + 5x² - 170x + 280

One of the factor of this polynomial is (x + 7)

By using remainder theorem

          5x²-30x+40

       -----------------------------------

x+7 | 5x³ + 5x² - 170x + 280

        5x³ + 35x²

               ----------------------------

                  -30x² -170x + 280

                  -30x² -210x

                            ------------------

                              40x + 280

                              40x + 280

                              ----------------

                                             0

So the polynomial we have is  

5x²- 30x + 40

divide by 5

x² - 6x + 8

(x-4)(x-2)

So the roots of the polynomial are -7 , 4 , 2

   

You might be interested in
The store owner tells the girls that half of the DVDS are out on loan. How many DVDS does the store own in total?​
patriot [66]

3

Step-by-step explanation:

i need help to

3 0
2 years ago
8:10 = 2:5<br> Is a true proportion?<br><br> O Yes<br> O No
Marina86 [1]

Answer:

Step-by-step explanation:

it is not.

7 0
3 years ago
Read 2 more answers
AsKevin Selma madelyn Louis
snow_tiger [21]
Very cool yes yes yes
7 0
2 years ago
ABD and CBD form a linear pair . if m ABD = 6x-12 and m CBD = x + 31 find the m ABD
otez555 [7]

Answer:

m∠ABD = 126°

Step-by-step explanation:

if both angles make a linear pair then their sum equals to 180°

you can solve for x

m∠ABD + m∠CBD = 180

6x-12 + x+31= 180

7x + 19 = 180

7x = 161

x=23; now solve for

m∠ABD = 6x - 12 = 6(23) - 12 = 126°

7 0
3 years ago
Read 2 more answers
On an analog clock the minute hand has moved 128 from 12 o clock. what number will it pass next​
Kitty [74]

Answer:

  5

Step-by-step explanation:

The numbers on the clock are separated by 30°, so the number 4 is at 120° after 12. The next number is 5, at 150°.

8 0
2 years ago
Other questions:
  • Subtract. (−8.3x+4)−(3.2x−5) Enter your answer, in simplified form, in the box.
    13·2 answers
  • use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine . . sin^6 x
    7·1 answer
  • 16b + 8 - 6<br> 16b + 2 = 2<br> Combine like terms<br> 16b = 0<br> Divide both sides by 16
    7·1 answer
  • 18 is 30 percent what is the total
    8·2 answers
  • Sử dụng phương pháp trung điểm, khi thu nhập bằng 7.500 đô la, thì độ co giãn của cầu theo giá trong khoảng từ 16 đô la đến 20 đ
    15·1 answer
  • Analyze the following problem. Was a mistake made? If so, find the error and correct it. Then, explain why it was a mistake.PLEA
    7·1 answer
  • (2.4+4n)+9 <br> SHOW ALL WORK!
    8·1 answer
  • Plzzzzzzzz helllllllppppppppp
    12·2 answers
  • Determine which of the lines, if any, are parallel or perpendicular. Explain.
    6·1 answer
  • Solve each question using square root property<br><br><br> (5x-1)^2=16
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!