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kipiarov [429]
3 years ago
15

Find m and n if the remainder when 8x^3+mx^2-6x+n if divided by (x-1) and (2x-3) are 2 and 8 respectively

Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
3 0

Answer:

we have:

8x³ + mx² - 6x + n

= 8x³ - 8x² + (m + 8)x²- (m + 8)x + (m + 2)x - (m + 2) + m + 2+ n

= 8x²(x - 1) + (m + 8)x(x - 1) + (m + 2)(x - 1) + (m + n + 2)

= (x - 1)[8x² + (m + 8)x + m + 2] + (m + n + 2)

because the remainder if divided by (x-1) is 2

=> m + n + 2 = 2

⇔ m + n = 0 (1)

we also have:

8x³ + mx² - 6x + n

= 8x³ - 12x² + (m + 12)x² - 3/2.x.(m + 12) + ( 12 + 3/2.m)x - (9/4.m +  18) + n +9/4m + 18              

= 4x²(2x - 3) + 1/2.(m + 12)x(2x - 3) + (3/2m + 12).1/2.(2x - 3) + 9/4m + n + 18

= (2x - 3)(4x² + (m + 12)/2.x + 3/4m + 6) + 9/4m + n + 18

 because the remainder if divided by  (2x - 3) is 8

=> 9/4m + n + 18 = 8

⇔ 9/4m + n = -10 (2)

from (1) and (2), we have:

m + n = 0

9/4m + n = -10

=> m = -8

      n = 8

Step-by-step explanation:

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What is the answer i need help 6(3+5)4
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Step-by-step explanation:

6(3+5)4

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Answer:

Height = 8 cm

You will need this formula (see attached):

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Source: http://www.1728.org/volcone.htm

Step-by-step explanation:

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2 years ago
a car moves 35 miles per hour travels a distance of 51.3 feet each second. about how far does a car travel in 7.1 seconds ?
Sergio039 [100]
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3 years ago
How is the series 9 + 13+ 17+ ... + 149 represented in summation notation?
VLD [36.1K]

Notice that

13 - 9 = 4

17 - 13 = 4

so it's likely that each pair of consecutive terms in the sum differ by 4. This means the last term, 149, is equal to 9 plus some multiple of 4 :

149 = 9 + 4k

140 = 4k

k = 140/4

k = 35

This tells you there are 35 + 1 = 36 terms in the sum (since the first term is 9 plus 0 times 4, and the last term is 9 plus 35 times 4). Among the given options, only the first choice contains the same amount of terms.

Put another way, we have

\displaystyle 9 + 13 + 17 + \cdots + 149 = \sum_{k=0}^{35} (9 + 4k)

but if we make the sum start at k = 1, we need to replace every instance of k with k - 1, and accordingly adjust the upper limit in the sum.

\displaystyle 9 + 13 + 17 + \cdots + 149 = \sum_{k-1=0}^{35+1} (9 + 4(k-1))

\displaystyle 9 + 13 + 17 + \cdots + 149 = \sum_{k=1}^{36} (5 + 4k)

7 0
2 years ago
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