Question

When the polynomial 2x^3-
kx^2 + (5k-3)x-8 is divided by x-2,
remainder is 14. Find the value of 'k'.​

Answer 1

Answer:

6 is the value

Step-by-step explanation:

Let f ( x ) = 2 x³ - k x² + 7 x - 1

If f ( x ) is divided be x - 2 ,

remainder = f ( 2 )

Hence :

f ( 2 ) = 5

⇒ 2 x³ - k x² + 7 x - 1 = 5

⇒ 2 . 2³ - k . 2² + 7 . 2 - 1 = 5

⇒ 16 - 4 k + 14 - 1 = 5

⇒ - 4 k = 5 - 13 - 16

⇒ - 4 k = - 24

⇒ k = - 24 / - 4

⇒ k = 6