Question

Find the value of k, if (x - k) is a factor of x6 – kx5 + x4 - kx3 + 3x – k + 4.

a) 2
b) -2
c) -3
d) 3​

Answer 1

Answer:

Correct question-

Find the value of k, if (x - k) is a factor of x⁶ - kx⁵ + x⁴ - kx³ + 3x - k + 4.

Solution-

Using factor theorem,

(x - k) = 0

→ x = k

put x = k in given polynomial.

→ (k)⁶ - k(k)⁵ + (k)⁴ - k(k)³ + 3(k) - k + 4 = 0

→ k⁶ - k⁶ + k⁴ - k⁴ + 3k - k + 4 = 0

→ 2k + 4 = 0

→ 2k = -4

→ k = -4/2

→ k = -2

Hence, option b) -2 is correct.

Answer 2

Answer:

the value of K =1 if (x-k) is the factor