Question

the remainder obtained by dividing kx2-3x+6 by(x-2) is the twice the remainder obtained by dividing 3x2 - 5x -k by (x-9) .find the value of k​

Answer 1

Please find the attachment

Answer 2

Answer:

• The value of k is 66.

Given:

• The remainder obtained by dividing kx³ - 3x + 6 by (x - 2) is the twice the remainder obtained by dividing 3x² - 5x - k by (x - 9).

To find:

• The value of k.

Solution:

By remainder theorem.

When p (x) = kx² - 3x + 6 is divided by ⠀⠀⠀x - 2

Remainder = p (2)

⠀⠀⠀⠀⠀⠀⠀ = 4k - 6 - 6

⠀⠀⠀⠀⠀⠀⠀ = 4k...(1)

When f (x) = 3x² - 5x - k is divided by x - 9

Remainder = f (9)

⠀⠀⠀⠀⠀⠀⠀= 3 (9)² - 5 (9) - k

⠀⠀⠀⠀⠀⠀⠀= 3 (81) - 45 - k

⠀⠀⠀⠀⠀⠀⠀= 243 - 45 - k

⠀⠀⠀⠀⠀⠀⠀= 198 - k...(2)

According to the given condition

4k = 2 (198 - k)

=> 4k = 396 - 2k

=> 6k = 396

=> k = 396/6

=> k = 66

Therefore, the value of k is 66.