Question

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

Answer 1

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.