Question

Find the value of k for which x – 2 is a factor of 4kx2 – √4x + 8.

Answer 1

Answer:

The required value of k is "–1/4"

Step-by-step explanation:

Given :

(x – 2) is a factor of polynomial 4kx² – √4x + 8

To find :

the value of k

Solution :

Let p(x) = 4kx² – √4x + 8

⇒ (x – 2) is a factor

 x – 2 = 0

 x = +2

Hence, 2 is a root of the given polynomial.

Since it's a root, when we substitute x = 2 the result is zero.

i.e., p(2) = 0

Put x = 2,

4k(2)² – √4(2) + 8 = 0

4k(4) – 2(2) + 8 = 0  [ √4 = 2 ]

16k – 4 + 8 = 0

16k + 4 = 0

 16k = –4

  k = –4/16

  k = –1/4

∴ The value of k is –1/4

Verification :

Put x = 2 and k = -1/4,

= 4(-1/4)(2)² – √4(2) + 8

= -1(4) – 2(2) + 8   [ √4 = 2 ]

= -4 – 4 + 8

= -8 + 8

= 0

The result is zero.