Question

Find the values of k so that (x-1) is a factor of k²x²-2kx-3.

Answer 1

$\underline\green{\bold{Answer:-}}$




Let ( x - 1 ) = 0

Then

=> x = 1

Put x = 1 in the given polynomial


P ( x ) = k^2x^2 - 2kx - 3

P ( 1 ) = k^2 ( 1 )^2 - 2k ( 1 ) - 3

=> k^2 - 2k - 3 = 0

=> k^2 - 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



Therefore the value of k is - 1 , 3





$\textbf{Hope it helps!}$

Answer 2

hey!


here is answer

here

x-1=0

hence

x=1


put the. value of. x in polynomial.


hence

${k}^{2} (1)^{2} - 2k(1) - 3$

${k}^{2} - 2k - 3$


it becomes in the form of quadratic equation

hence factorize it

${k}^{2} - 3k + k - 3$


$k(k - 3) + 1(k - 3)$


$\bf{(k + 1)(k - 3)}$


hence

k+1=0

k=-1

or

k-3=0

k=3

hope it helps

thanks