Question

the value of K for which 2x+1 is a factor of x²-kx+4
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Answer 1

Answer:

k = -17/2

Step-by-step explanation:

let f(x) = x²-kx+4

given that (2x+1) is a factor of f(x)

so, take 2x+1 = 0

          => 2x = -1

          => x = -1/2

=> by remainder theorem  , f(-1/2) = 0

ie, => (-1/2)²-k(-1/2)+4 = 0

    => (1/4)+(k/2)+4 = 0

    => 1+2k+16 = 0    (multiply by 4 on both sides)

    => 2k+17 = 0  

    => 2k = -17

    => k = -17/2