Find the value of k if (x-3) is a factor of k square × x square - k × x-2

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Solution

Given equation K^2 x^2-kx-2=0

Put x=3 ( in above equation)

9k^2-3k-2=0
(here -3k can be written as (-6k+3k) )

9k^2-6k+3k-2=0
(3k can take out side from
9k^2 and 6k)
3k (3k-2)+1 (3k-2)=0

3k-2 can be taken out side

(3k-2)(3k+1)=0

From the above equation

If 3k-2=0 Then
3k=2

K= 2/3

If 3k+1=0
3k=-1
K=-1/3

Then k=(-1/3)
Required value of k is

2/3 or (-1/3)

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