Question

I will thank uoy if you will be fast
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

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:

-2

Step-by-step explanation

step I)

       let's say g(x)=x-k and f(x) = x^6 - kx^5 + x^4 - kx^3 + 3x - k + 4

step II)

          find the zeros of g(x): -

                      g(x)=x-k, x-k=0  :. thus, x=k

step III)

          now replace x with k and find the value of K

          f(X)= k^6 - k^6 + k^4 - K^4 + 3k - k + 4 = 0

                2k + 4 = 0

                  k = -4/2 = -2          :- the solution is -2