Question

Find the values of k for which the roots are real and equal in each of the following equations:
(4 - k)x2 + (2k + 4)x + (8k + 1) = 0​

Answer 1

Answer:

2k answer. i hope you are help

Answer 2

Step-by-step explanation:

Here, a = (4 - k), b = (2k + 4) and c = (8k + 1)

As we know that D = b2 - 4ac

Putting the value of a = (4 - k), b = (2k + 4) and c = (8k + 1)

= (2k + 4)2 - 4 x (4 - k) x (8k + 1)

= 4k2 + 16k - 16 - 4(4 + 31k - 8k2)

= 4k2 + 16k - 16 - 16 - 124k + 32k2

= 36k2 - 108k + 0

= 36k2 - 108k

The given equation will have real and equal roots, if D = 0

Thus,

36k2 - 108k = 0

18k(2k - 6) = 0

k(2k - 6) = 0

Now factorizing of the above equation

k(2k - 6) = 0

So, either

k = 0

or

2k - 6 = 0

2k = 6

k = 6/2 = 3

Therefore, the value of k = 0, 3.