Question

P(x)=2x³-x²+kx-4.
Divide p(x) by x-2 remainder will be 6. Find k

Answer 1

Answer:

k = -1

Concept used:

p(x) divided by (x - a) leaves remainder p(a).

Step-by-step explanation:

p(x) = 2x³ - x² + kx - 4 = 0

Here, p(x) divided by (x - 2) leaves remainder 6.

∴ p(2) = 6

⇒ 2(2)³ - (2)² + k(2) - 4 = 6

⇒ 2 × 8 - 4 + 2k - 4 = 6

⇒ 16 - 4 + 2k - 4 = 6

⇒ 2k + 8 = 6

⇒ 2(k + 4) = 2 × 3

⇒ k + 4 = 3

⇒ k = 3 - 4

⇒ k = -1

Thus the value of k is -1.