Question

find the value of k if (x-3) is factor of k2 x2-kx-2

Answer 1

Hey

Here is your answer,

( x-3 ) is a factor of k^2 x^2 - kx - 2 = 0

X-3 = 0
X = 3

k^2 x^2 - kx - 2 = 0
(3)^2 k^2 - 3k - 2 = 0
9k^2 - 3k - 2 = 0
9k^2 - 6k + 3k - 2 = 0
3k ( 3k-2 ) + 1 ( 3k-2 ) = 0
( 3k-2 ) ( 3k+1 ) = 0
3k-2 = 0
k = 2/3
3k+1 = 0
k = -1/3

Hope it helps you!

Answer 2

( X - 3 ) is a factor of the given polynomial p ( x ).



So,


X - 3 = 0


X = 3


P ( X ) = K² X² - KX - 2



P (3) = K² (3)² - K × 3 - 2




=> K² × 9 - 3K - 2



=> 9K² - 3K - 2



=> 9K² - 6K + 3K - 2



=> 3K ( 3K - 2 ) + 1 ( 3K - 2)



=> ( 3K - 2 ) ( 3K + 1 ) = 0



=> ( 3K - 2 ) = 0 OR ( 3K + 1 ) = 0



=> K = 2/3 OR K = -1/3