Question

Find the value of k so that(x-1) is a
factor of k^2x^2 - 2kx-3​

Answer 1

Answer:

k = 1,-3

Step-by-step explanation:

Let p( x ) = k² x² - 2kx - 3

If ( x + 1 ) is a factor p( x ) then

Remainder p ( - 1 ) = 0

k² ( - 1 )² - 2 k ( - 1 ) - 3 = 0

k² + 2k - 3 = 0

k² - k + 3k - 3 = 0

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

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

k - 1 = 0 or k + 3 = 0

k = 1 or k = - 3

Answer 2

Answer :-

k = - 1 or k = 3

Solution :-

Let f( x ) = k²x² - kx - 3

(x - 1) is a factor of f( x )

Finding zero of (x - 1)

⇒ x - 1 = 0

⇒ x = 1

By factor theorem

⇒f( 1 ) = 0

⇒ k²( 1 )² - 2k( 1 ) - 3 = 0

⇒ k²( 1 ) - 2k - 3 = 0

⇒ k² - 2k - 3 = 0

⇒ k² - 3k + k - 3 = 0

⇒ k(k - 3) + 1(k - 3) = 0

⇒ (k + 1)(k - 3) = 0

⇒ k + 1 = 0 or k - 3 = 0

⇒ k = - 1 or k = 3

Hence, the value of k is - 1 or 3.