Question

find the value of k if 2x+1 is a factor of 4xsquare -kx +k

Answer 1

Heya !!!






( 2X + 1) is a factor of the given polynomial.




( 2X + 1) = 0




X = -1/2




P(X) = 4X² - KX + K




P(-1/2) = 4 × (-1/2)² - K × -1/2 + K





=> 4 × 1/4 + K/2 + K = 0




=> 1 + K/2 + K = 0





=> 2 + K + 2K = 0




=> 3K = -2





=> K = -2/3




★ HOPE IT WILL HELP YOU ★

Answer 2

          Let f(x) = 4x^2 - kx + k 



Given (2x + 1) is a factor of f(x) , by factor Theorem,

f(-1/2) = 0 


⇒ 4x^2 - kx + k = 0 

⇒ 4(-1/2)^2 - k(-1/2) + k = 0 

⇒ 4(1/4) + k/2 + k = 0 

⇒ 1 + k/2 + k = 0 

⇒ k/2 + k = -1 

⇒ (k + 2k)/2 =  -1

⇒ 3k = -2 

⇒k = -2/3 





i hope this will help you


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