Question

Find the value of k, if p(x) = x 3 –kx 2 + 11x -6 and (x-1) is a factor of p(x)

Answer 1

Answer:

According to factor theorem, if (x-a) is a factor of f(x) then f(a)=0

Here,

Since (x-1) is factor of p(x), p(1)=0 or, 1^3 - k×1^2 + 11×1 -6 =0

or, 6-k=0 or k=6

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

∵ (x - 1) is a factor of p(x)

∴ By factor theorem, we are p(1) = 0

⇒ (1)³ - k(1)² + 11(1) - 6 = 0

⇒1 - k + 11 - 6 = 0

⇒ 6 - k = 0

⇒k = 6

Hence, the value of k is 6.