find the values os a and b so that the polynomial x3+10x2+ax+b is exactly divisible by (x-1) and (x+2)

Mathematics

1 answer:

ad-work [718]3 years ago

8 0

Answer:

a = 7 and b = - 18

Step-by-step explanation:

If (x - 1) is a factor of f(x) then x = 1 is a root and f(1) = 0, thus

f(1) = 1³ + 10(1)² + a + b = 0 and

1 + 10 + a + b = 0 ⇒ a + b = - 11 → (1)

Similarly if

(x + 2) is a factor then x = - 2 is a root and f(- 2) = 0

f(- 2) = (- 2)³ + 10(- 2)² - 2a + b = 0, thus

- 8 + 40 - 2a + b = 0 ⇒ - 2a + b = - 32 → (2)

Solve (1) and (2) simultaneously

Subtract (1) from (2)

- 3a = - 21 ( divide both sides by 3)

a = 7

Substitute a = 7 in (1)

7 + b = - 11 ⇒ b = - 11 - 7 = - 18

The required polynomial is

f(x) = x³ + 10x² + 7x - 18

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The shower block on the campsite has an area of 144 m2 The length of the shower block is 24 m. What is the width? m

skad [1K]

Area= length*width

Plug in what you know.

144= 24*width

Divide both sides by 24.

width= 6 meters.

I hope this helps!
~kaikers

4 0

3 years ago

Plz help this is due tonight and I have no clue :(

motikmotik

Section 1:

using this format we can determine what the answer is:

42 105
—— • ——-
100 x

(the spacing may be off but imagine two separate fractions)

first multiply 100 by 105 to get 10,500

then divide by 42 to get 250

this means that sasha’s book has 250 pages

section b:

using the same formula we can solve this problem:

first we need to multiply 250 by 2 to get the total cost of both tickets

175 x
—— • ——
100 500

(again spacing may be off but think of two separate fractions)

then multiply 500 by 175 to get 87,500

then divide by 100 to get 875

to find the profit subtract 875-500

this means he will make $375 profit

conclusion:

sasha’s book has 250 pages

trevor will make $375 profit

this is the method my teacher taught me last year so it should be right, hope this helps and please mark brainliest!!

8 0

3 years ago

3 consecutive odd integers such that the sum of twice the first and three times the second is 55 more than twice the third

den301095 [7]

Answer:

Consecutive odd integers are 19 , 21 & 23

Step-by-step explanation:

Let the first 3 consecutive odd intergers be x , (x + 2) and (x + 4).

According to the question,

$2x + 3(x + 2) = 2(x + 4) + 55$