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
arsen [322]
2 years ago
11

Find number a and k so that x-2 is afactorOF F(x)=x4-2ax tax-X+k and F(-1)=3​

Mathematics
1 answer:
Slav-nsk [51]2 years ago
3 0

Question:

Find numbers a and k so that x-2 is a factor of

f(x)=x^4-2ax^3+ax^2- x+k

and

f(-1)=3

Answer:

k = -2 and a=1

Step-by-step explanation:

Given

f(x)=x^4-2ax^3+ax^2- x+k

Factor:\ x - 4

f(-1)=3

Required

Find a and k

For f(-1)=3

Substitute -1 for x

f(x)=x^4-2ax^3+ax^2- x+k

f(-1) = (-1)^4 - 2a *(-1)^3 + a*(-1)^2 - (-1) + k

f(-1) = 1 - 2a *-1 + a*1 +1 + k

f(-1) = 1 +2a + a +1 + k

f(-1) = 2 +3a + k

Substitute 3 for f(-1)

3 = 2 +3a + k

Collect Like Terms

3 - 2 = 3a + k

1 = 3a + k

Also:

If x - 2 is a factor, then

f(2) = 0

Substitute 2 for x and 0 for f(x)

f(x)=x^4-2ax^3+ax^2- x+k

0 = 2^4 - 2a * 2^3 + a * 2^2 - 2 + k

0 = 16 - 2a * 8 + a * 4 - 2 + k

0 = 16 - 16a + 4a - 2 + k

0 = 16 - 12a - 2 + k

Collect Like Terms

2 - 16 = - 12a + k

-14 = k - 12a

k = 12a - 14

Substitute 12a - 14 for k in 1 = 3a + k

1 = 3a + 12a - 14

1 = 15a - 14

Collect Like Terms

15a = 1 + 14

15a = 15

Solve for a

a = \frac{15}{15}

a=1

Substitute 1 for a in k = 12a - 14

k = 12 * 1 - 14

k = 12 - 14

k = -2

You might be interested in
15 men can dig a trench of 90 m long in
jeyben [28]

Answer:

1.5 hours= 1hour and 30 minutes

Step-by-step explanation:

90÷15=6

6÷2=3

48÷16=3

3÷2=1.5

5 0
3 years ago
Read 2 more answers
1.) Find f(4) for f(x) = 3x - 4
Keith_Richards [23]
The answer is f(4)=8 hope this helps can I have brain list pls I really need it right now
8 0
3 years ago
Need help answering this question within the next 2 hours...Thanks!
just olya [345]
Subsitue a number for x then solve for y  then graph the point repeat untill u have a parabola
6 0
3 years ago
What is the vertex of the absolute value function defined by ƒ(x) = |x + 5| + 7?
Mandarinka [93]
<span>hello :
اthe vertex of the absolute value function defined by ƒ(x) = |x + 5| + 7 is :
</span>(-5,7) because when : x= - 5    ...f(-5) = |- 5 + 5| + 7 = 0+ 7 = 7
7 0
3 years ago
Read 2 more answers
PLEASE HELP!
blsea [12.9K]

Answer:

He was correct

Step-by-step explanation:

100÷ 19.678= 5

5 meters for seconds

8 0
3 years ago
Other questions:
  • What is the domain of f(x)=3x/x-1?
    7·2 answers
  • Name the minor arc and find its measure.
    10·1 answer
  • A pool in the shape of a rectangle has a perimeter of 80 ft. The pool is 8 feet wide than it is long. Find the length and width
    6·1 answer
  • The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
    14·2 answers
  • Can some one help me with total surface area of rectangular prism plz
    6·1 answer
  • If x≠4 and x≠-4, the fraction x^2-8x+16/x^2-16 can be simplified to what?
    14·1 answer
  • Anyone good at finding surface area and volume?
    10·1 answer
  • Is 120 divisible by 3 and 4
    15·2 answers
  • What is the equation of the line that passes through the point (-2,-1) and has a slope of 1?
    11·1 answer
  • Simplify 2 x 4x x 2y​
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!