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
qaws [65]
2 years ago
15

Consider the cubic function f(x) = x^3 + ax^2 + bx + 4 where (a) and (b) are constants. When f(x) is divided by x-3, the remaind

er is 10. When f (x) is divided by x+1, the remainder is 6.
Show that a = -1 and b = -4
Mathematics
1 answer:
Debora [2.8K]2 years ago
8 0

Answer:

see explanation

Step-by-step explanation:

Using the Remainder theorem

If f(x) is divided by (x - h) then f(h) = remainder, thus

f(3) = 3³ + a(3)² + b(3) + 4 = 10, that is

27 + 9a + 3b + 4 = 10

9a + 3b + 31 = 10 ( subtract 31 from both sides )

9a + 3b = - 21 → (1)

f(- 1) = (- 1)³ + a(- 1)² + b(- 1) + 4 = 6, that is

- 1 + a - b + 4 = 6

a - b + 3 = 6 ( subtract 3 from both sides )

a - b = 3 → (2)

Rearrange (2) expressing a in terms of b

a = 3 + b → (3)

Substitute a = 3 + b into (1)

9(3 + b) + 3b = - 21 ← distribute and simplify left side

27 + 9b + 3b = - 21

12b + 27 = - 21 ( subtract 27 from both sides )

12b = - 48 ( divide both sides by 12 )

b = - 4

Substitute b = - 4 into (3)

a = 3 - 4 = - 1

Hence a = - 1 and b = - 4

You might be interested in
Find the value of d.
Ket [755]
First find the value or (DEA)
For this you will have to use the Pythagorean theory,
{a}^{2} + {b}^{2} = {c}^{2}
C is mainly the hypotenuse,
Meaning you either want to find A or B,

Since the hypotenuse has two segments, both values are 10, then just add them together making it 20,

Then 16 will be A or B, in this case it will be A,

To find a you must first move A to the other side by doing the opposite,
{b}^{2} = {c}^{2} - {a}^{2}
Now plug in the values,
{b}^{2} = {20}^{2} - {16}^{2}
{b}^{2} = 400 - 256
{b}^{2} = 144
Now just find the square root of both factors,
\sqrt{ {b}^{2} } = \sqrt{12}
The value of (DEA) is,
b = 12
Now we want to find (d)
Since 12 is the value of the base, then divide it 2 to find (DE), after just repeat the whole process but with the value of hypotenuse 10 instead of 20 since we want to find the smaller triangle,
{a}^{2} = {c}^{2} - {b}^{2}
Now plug in the value
{a}^{2} = {10}^{2} - {6}^{2}
{a}^{2} = 100 - 36
{a}^{2} = 64
Now find the square root of both factors,
\sqrt{ {a}^{2} } = \sqrt{64}
a = 8

The value of (d) is (8)

Hope this helped
:D
4 0
2 years ago
What is 1/8 times 3/4
Serga [27]
Hi there

1/8 * 3/4

Remember: When you are multiply two fractions together all you have to do is multiply the numerator by the denominator.

Answer : 3/32

I hope that's help !
4 0
3 years ago
Louisa starts training for cross country. She records how far she can run without stopping each week.
PIT_PIT [208]

Answer:

I need more info!

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
I need help please help
Rufina [12.5K]
A. pat x-10 is a negative
6 0
2 years ago
GUYS PLEASE HELP ME I REALLY DON'T UNDERSTAND THIS TASK!!!!!!! IT'S VERY IMPORTANT FOR ME!!!!! DISTANCE BETWEEN TWO TOWNSHIPS, E
Dimas [21]
For this problem, you know that the first walker will arrive 2 hours before the second, and increases his speed by 2 times the second walker. You also know there is a distance of 24 km. So up until some time x, the two walkers have to be going the same speed. If the first walker increases speed by two times the speed per hour, and arrives two hours earlier, then his initial speed will be 20 km/h, because after 2 hours, he will have an increase of 4 km/hr, and the second will have an increase of 2 km/h, thereby making the first arrive 2 hours earlier, if that makes sense.
5 0
3 years ago
Other questions:
  • A bag contains three red marbles and two blue marbles. Marcus reaches in and pulls out a marble, does not replace it, but then r
    6·1 answer
  • Round each number to the nearest tenth. What is the best estimate for the difference of 264.72 128.49? A. 137 B. 136.3 C. 136.2
    9·2 answers
  • Find the sum and express it in simplest form.<br> (-73-y + 1) + (-7y3 - 6y)
    8·1 answer
  • Tori has a one-gallon container to fill with lemonade. She uses the standard recipe. How much concentrate does she need? (one ga
    9·1 answer
  • Part A.
    10·1 answer
  • A movie theater sends out a coupon for ​% off the price of a ticket. Write an equation for the​ situation, where y is the price
    8·1 answer
  • 3 . Based on the histogram above, how are the data distributed, and where is the mean located in relation to the median?
    12·1 answer
  • How does the underlined sentence shaped and refine the key idea that Caesar avoided the wrath of the dictator sulla it indicates
    10·1 answer
  • PLEASE HELP MEE!!! I WILL GIVE YOU THE BRAINLIEST
    8·1 answer
  • 3/5 + 7/8 + 3/10
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!