Question

if 2x+1 is a factor of the polynomial 4x²-kx+k , then find the value of k

Answer 1

Given,

2x+1 is a factor of the polynomial 4x²-kx+k

To Find,

The value of k.

Solution,

Since 2x+1 is a factor of the given polynomial

2x+1 = 0

x = -1/2

Now, this value of x will satisfy the given polynomial

4(-1/2)²-k(-1/2)+k = 0

1+k/2+k = 0

3k/2 = -1

k = -2/3

Hence, the value of k is -2/3.

Answer 2

Given:

2x+1 is a factor of the polynomial 4x²-kx+k

To Find:

Find the value of k

Solution:

f(x) = 4x² - kx + k

g(x) =2x+1

putting 2x + 1 = 0, we get

x = -1/2

Since it's a factor, f(-1/2) = 0

4(-1/2)² - k(-1/2) + k = 0

4x1/4 + 1/2k + k = 0

1 + (1+2k/2) = 0

3/2k = -1

k = -2/3

Hence, k has a value of -2/3.