CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

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


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.

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image