Question

# If 2x+ 1 is a factor of 4x ^ 2-kx-k, find the value of k.

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Solution

## Dear student, 2x+1 is a factor. So we can write (2x+1)m= 4x²-kx-k Where m is any number. So if we equate 4x²-kx-k=0, We can write; (2x+1)m=0 If product of two numbers is zero, then one of the number must be zero. For example, 6×0=0; So we assume (2x+1)=0 or m=0 X=-1/2 So if we substitute x=-1/2, then 4x²-kx-k=0 i.e x=(-1/2) is a zero of the polynomial 4x²-kx-k. So, 4(-1/2)²-k(-1/2)-k=0 = 4(1/4)+k/2-k=0 =1+k/2-k=0 =1-k/2=0 =1=k/2 =K=2 Please read carefully 3 or 4 times to understand better. Thank you.

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