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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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which equation represents an exponential function that passes through the point (2, 80)? f(x) = 4(x)5 f(x) = 5(x)4 f(x) = 4(5)x
pav-90 [236]

we know that

if the exponential function passes through the given point, then the point must satisfy the equation of the exponential function

we proceed to verify each case  if the point (2,80) satisfied the exponential function

<u>case A</u>  f(x)=4(x^{5})

For x=2 calculate the value of y in the equation and then compare with the y-coordinate of the point

so

f(2)=4(2^{5})=128

128\neq 80

therefore

the exponential function  f(x)=4(x^{5}) not passes through the point (2,80)

<u>case B</u>  f(x)=5(x^{4})

For x=2 calculate the value of y in the equation and then compare with the y-coordinate of the point

so

f(2)=5(2^{4})=80

80=80

therefore

the exponential function f(x)=5(x^{4}) passes through the point (2,80)

<u>case C</u>  f(x)=4(5^{x})

For x=2 calculate the value of y in the equation and then compare with the y-coordinate of the point

so

f(2)=4(5^{2})=100

100\neq 80

therefore

the exponential function f(x)=4(5^{x}) not passes through the point (2,80)

<u>case D</u>  f(x)=5(4^{x})

For x=2 calculate the value of y in the equation and then compare with the y-coordinate of the point

so

f(2)=5(4^{2})=80

80=80

therefore

the exponential function f(x)=5(4^{x}) passes through the point (2,80)

therefore

<u>the answer is</u>

f(x)=5(x^{4})

f(x)=5(4^{x})

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To solve this polynomial equation, set it equal to zero first.

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